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1
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Evaluate  ∫dx16+9x2−−−−−−√ ∫dx16+9x2

Select one:
a.
23ln(secθ+tanθ)+c23ln(secθ+tanθ)+c
b.
23ln(secθ−tanθ)+c23ln(secθ−tanθ)+c
c.
13ln(secθ−tanθ)+c13ln(secθ−tanθ)+c
d.
13ln(secθ+tanθ)+c13ln(secθ+tanθ)+c

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Evaluate  ∫dxxx2−2x−−−−−√ ∫dxxx2−2x

Select one:
a.
2sinθ+c2sinθ+c
 b.
2sin2θ+c2sin2θ+c
c.
sin2θ+csin2θ+c
d.
sinθ+csinθ+c

Question 3
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Evaluate  ∫xexdx∫xexdx

Select one:
a.
−xex−ex+C−xex−ex+C
b.
−xex+ex+C−xex+ex+C
c.
xex+ex+Cxex+ex+C
d.
xex−ex+Cxex−ex+C

Question 4
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∫
Evaluate   x2−9dx−−−−−−√x∫x2−9dxx
Select one:
a.
3tanθ+3θ+c3tanθ+3θ+c
b.
3tanθ−3θ+c3tanθ−3θ+c
c.
5tanθ+3θ+c5tanθ+3θ+c
d.
5tanθ−3θ+c5tanθ−3θ+c

Question 5
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Evaluate  ∫x2x+1dx−−−−−−−√∫x2x+1dx

Select one:
a.
2z77+3z55+2z33+c2z77+3z55+2z33+c

b.
2z77+4z55+z33+c2z77+4z55+z33+c
c.
2z77+4z55+2z33+c2z77+4z55+2z33+c

d.
z77+4z55+2z33+cz77+4z55+2z33+c

Question 6
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 Question text
Evaluate  ∫(4−x)x−−√3dx∫(4−x)x3dx

Select one:
a.
3z4−47z7+c3z4−47z7+c
b.
3z4−37z7+c3z4−37z7+c
c.
4z4−37z7+c4z4−37z7+c
d.
4z4−47z7+c4z4−47z7+c
Question 7
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Evaluate  ∫exsin x dx∫exsin x dx

Select one:
a.
13ex(sin x+cos x)+C13ex(sin x+cos x)+C

b.
12ex(sin x+cos x)+C12ex(sin x+cos x)+C

c.
12ex(sin x−cos x)+C12ex(sin x−cos x)+C

d.
13ex(sin x−cos x)+C13ex(sin x−cos x)+C

Question 8
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Evaluate  ∫xcosx dx∫xcosx dx

Select one:
a.
−xsinx−cosx+C−xsinx−cosx+C
b.
−xsinx+cosx+C−xsinx+cosx+C
c.
xsinx−cosx+Cxsinx−cosx+C
d.
xsinx+cosx+Cxsinx+cosx+C

Question 9
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Evaluate  ∫xcosx dx∫xcosx dx

Select one:
a.
−xsinx−cosx+C−xsinx−cosx+C
b.
−xsinx+cosx+C−xsinx+cosx+C
c.
xsinx+cosx+Cxsinx+cosx+C
d.
xsinx−cosx+Cxsinx−cosx+C
Question 10
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Evaluate  ∫x sec2 x dx∫x sec2 x dx

Select one:
a.
xtanx+ln|secx|+Cxtanx+ln|secx|+C
b.
−xtanx+ln|secx|+C−xtanx+ln|secx|+C
c.
xtanx−ln|secx|+Cxtanx−ln|secx|+C
d.
−xtanx−ln|secx|+C−xtanx−ln|secx|+C

Question 11
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Evaluate∫dx(4−x2)32∫dx(4−x2)32

Select one:
a.
−tanθ+C−tanθ+C
b.
14tanθ+C14tanθ+C

c.
4tanθ+C4tanθ+C
 d.
tanθ+Ctanθ+C

Question 12
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Evaluate  

∫dx(x2+9)2(trigosubs) ∫dx(x2+9)2(trigosubs)

Select one:
a.
19(θ+sinθcosθ)+c19(θ+sinθcosθ)+c
b.
154(θ+sinθcosθ)+c154(θ+sinθcosθ)+c
c.
127(θ+sinθcosθ)+c127(θ+sinθcosθ)+c
d.
13(θ+sinθcosθ)+c13(θ+sinθcosθ)+c

Question 13
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Evaluate  ∫xcsc2xdx∫xcsc2xdx

Select one:
 a.
cotx+ln(cscx−cotx)+Ccotx+ln(cscx−cotx)+C
b.
−cotx+ln(cscx−cotx)+C−cotx+ln(cscx−cotx)+C
c.
cotx−ln(cscx−cotx)+Ccotx−ln(cscx−cotx)+C
d.
−cotx−ln(cscx−cotx)+C−cotx−ln(cscx−cotx)+C

Question 14
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Evaluate  

∫xx−2−−−−√dx ∫xx−2dx

Select one:
a.
z55+z35+Cz55+z35+C
b.
2z53+z35+C2z53+z35+C
c.
z53+4z33+Cz53+4z33+C

d.
2z55+4z33+C2z55+4z33+C

Question 15
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Evaluate  ∫x2e−xdx∫x2e−xdx

Select one:
a.
−x2e−x+2[−e−x(x+1)]+C−x2e−x+2[−e−x(x+1)]+C
b.
x2e−x+2[−e−x(x+1)]+Cx2e−x+2[−e−x(x+1)]+C
c.
−x2e−x−2[−e−x(x+1)]+C−x2e−x−2[−e−x(x+1)]+C
d.
x2e−x−2[−e−x(x+1)]+Cx2e−x−2[−e−x(x+1)]+C

Question 16
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Evaluate  

∫(3x2+8x−12)x3+7x2+12xdx ∫(3x2+8x−12)x3+7x2+12xdx

Select one:
a.
−lnx−3ln(x+3)+ln(x+4)+c−lnx−3ln(x+3)+ln(x+4)+c
b.
−lnx+3ln(x+3)+ln(x+4)+c−lnx+3ln(x+3)+ln(x+4)+c
c.
lnx+3ln(x+3)+ln(x+4)+clnx+3ln(x+3)+ln(x+4)+c
d.
−lnx+3ln(x+3)−ln(x+4)+c−lnx+3ln(x+3)−ln(x+4)+c
Question 17
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Evaluate  ∫dxex−1−−−−√ ∫dxex−1

Select one:
a.
θ+cθ+c
b.
2θ+c2θ+c
c.
3θ+c3θ+c
d.
4θ+c4θ+c
Question 18
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Evaluate  ∫(x−1)dxx2+5x+6∫(x−1)dxx2+5x+6
Select one:
a.
3ln(x+2)+ln(x+3)+c3ln(x+2)+ln(x+3)+c
b.
ln(x+2)+4ln(x+3)+cln(x+2)+4ln(x+3)+c
c.
3ln(x+2)+4ln(x+3)+c3ln(x+2)+4ln(x+3)+c
d.
ln(x+2)+ln(x+3)+cln(x+2)+ln(x+3)+c

Question 19
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Evaluate  ∫x sin x dx∫x sin x dx

Select one:
a.
x cos x−sin x+Cx cos x−sin x+C
b.
−x cos x+sin x+C−x cos x+sin x+C
c.
x cos x+sin x+Cx cos x+sin x+C
d.
−x cos x−sin x+C−x cos x−sin x+C

Question 20
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 Question text
Evaluate  ∫x2sin2xdx∫x2sin2xdx

Select one:
a.
−12x2cos2x+12xsin2x+14cos2x+c−12x2cos2x+12xsin2x+14cos2x+c
b.
12x2cos2x+12xsin2x+14cos2x+c12x2cos2x+12xsin2x+14cos2x+c

c.
−12x2cos2x−12xsin2x+14cos2x+c−12x2cos2x−12xsin2x+14cos2x+c
d.
12x2cos2x−12xsin2x+14cos2x+c12x2cos2x−12xsin2x+14cos2x+c

Question 21
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∫
Evaluate   (5y−4)dyy3+4y2∫(5y−4)dyy3+4y2

Select one:
a.
1y+32lny+32ln(y+4)+c1y+32lny+32ln(y+4)+c
b.
1y−32lny+32ln(y+4)+c1y−32lny+32ln(y+4)+c
c.
1y−32lny−32ln(y+4)+c1y−32lny−32ln(y+4)+c
d.
1y+32lny−32ln(y+4)+c1y+32lny−32ln(y+4)+c

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Evaluate  

∫sinθcos2θ1+cosθ−−−−−−√dθ ∫sinθcos2θ1+cosθdθ

Select one:
a.
−2z55+4z33−2z+c−2z55+4z33−2z+c
b.
2z55−4z33−2z+c2z55−4z33−2z+c
c.
2z55+4z33−2z+c2z55+4z33−2z+c
d.
−2z55−4z33−2z+c−2z55−4z33−2z+c
Question 23
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Evaluate  ∫x2exdx∫x2exdx

Select one:
a.
x2ex−2xex−2ex+Cx2ex−2xex−2ex+C
b.
x2ex+2xex−2ex+Cx2ex+2xex−2ex+C
 c.
x2ex−2xex+2ex+Cx2ex−2xex+2ex+C
d.
−x2ex−2xex−2ex+C−x2ex−2xex−2ex+C

Question 24
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Evaluate  

∫(x−−√+1)14dx ∫(x+1)14dx

Select one:
a.
49(z+1)94−45(z+1)54+c49(z+1)94−45(z+1)54+c
b.
89(z+1)94−25(z+1)54+c89(z+1)94−25(z+1)54+c
c.
49(z+1)94−25(z+1)54+c49(z+1)94−25(z+1)54+c
d.
89(z+1)94−45(z+1)54+c89(z+1)94−45(z+1)54+c

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Evaluate  

∫(x+1)2x−1−−−−−√dx ∫(x+1)2x−1dx

Select one:
a.
110(z)5−16(z)3+c110(z)5−16(z)3+c
b.
310(z)5+16(z)3+c310(z)5+16(z)3+c
c.
310(z)5−16(z)3+c310(z)5−16(z)3+c
d.
110(z)5+16(z)3+c110(z)5+16(z)3+c

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∫
Evaluate   (x2−5x+3)dxx3−4x2+3x∫(x2−5x+3)dxx3−4x2+3x

Select one:
a.
−ln x−12ln(x−3)+12ln(x+1)+c−ln x−12ln(x−3)+12ln(x+1)+c
b.
ln x−12ln(x−3)+12ln(x+1)+cln x−12ln(x−3)+12ln(x+1)+c
c.
ln x+12ln(x−3)+12ln(x+1)+cln x+12ln(x−3)+12ln(x+1)+c
d.
ln x−12ln(x−3)−12ln(x+1)+cln x−12ln(x−3)−12ln(x+1)+c
Question 27
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Evaluate  

∫(lnsin2x)(cos2x)dx ∫(lnsin2x)(cos2x)dx

Select one:
a.
12sin2x.lnsin2x+12sin2x+C12sin2x.lnsin2x+12sin2x+C
b.
12sinx.lnsin2x−12sin2x+C12sinx.lnsin2x−12sin2x+C
c.
12sin2x.lnsin2x−12sin2x+C12sin2x.lnsin2x−12sin2x+C
d.
−12sin2x.lnsin2x+12sin2x+C−12sin2x.lnsin2x+12sin2x+C
Question 28
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Evaluate  ∫ln(x−−√+1)dx∫ln(x+1)dx

Select one:
a.
z2ln(z+1)−z22+z−ln(z+1)+cz2ln(z+1)−z22+z−ln(z+1)+c
 b.
−z2ln(z+1)−z22+z−ln(z+1)+c−z2ln(z+1)−z22+z−ln(z+1)+c
c.
z2ln(z+1)+z22+z−ln(z+1)+cz2ln(z+1)+z22+z−ln(z+1)+c
d.
−z2ln(z+1)+z22+z−ln(z+1)+c−z2ln(z+1)+z22+z−ln(z+1)+c
Question 29
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∫
Evaluate   x−−√dx(4+x)2∫xdx(4+x)2

Select one:
a.
12θ+14sin2θ+c12θ+14sin2θ+c
b.
12θ+34sin2θ+c12θ+34sin2θ+c
c.
12θ−34sin2θ+c12θ−34sin2θ+c
d.
12θ−14sin2θ+c12θ−14sin2θ+c

Question 30
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Evaluate  ∫xe3xdx∫xe3xdx

Select one:
a.
13xe3x−19e3x+C13xe3x−19e3x+C

b.
19xe3x−13e3x+C19xe3x−13e3x+C

c.
13xe3x−13e3x+C13xe3x−13e3x+C

d.
19xe3x−19e3x+C

Question 1
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Evaluate  ∫x2exdx∫x2exdx

Select one:
a.
x2ex+2xex−2ex+Cx2ex+2xex−2ex+C
b.
−x2ex−2xex−2ex+C−x2ex−2xex−2ex+C
c.
x2ex−2xex+2ex+Cx2ex−2xex+2ex+C
d.
x2ex−2xex−2ex+Cx2ex−2xex−2ex+C

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Evaluate  ∫xcsc2xdx∫xcsc2xdx

Select one:
a.
−cotx−ln(cscx−cotx)+C−cotx−ln(cscx−cotx)+C
b.
−cotx+ln(cscx−cotx)+C−cotx+ln(cscx−cotx)+C
c.
cotx−ln(cscx−cotx)+Ccotx−ln(cscx−cotx)+C
d.
cotx+ln(cscx−cotx)+Ccotx+ln(cscx−cotx)+C

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Evaluate  ∫xcosx dx∫xcosx dx

Select one:
a.
xsinx+cosx+Cxsinx+cosx+C
b.
xsinx−cosx+Cxsinx−cosx+C
c.
−xsinx−cosx+C−xsinx−cosx+C
d.
−xsinx+cosx+C−xsinx+cosx+C
Question 4
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Evaluate  ∫xexdx∫xexdx

Select one:
a.
−xex−ex+C−xex−ex+C
b.
xex−ex+Cxex−ex+C
c.
xex+ex+Cxex+ex+C
d.
−xex+ex+C−xex+ex+C

Question 5
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Evaluate  ∫x2sin2xdx∫x2sin2xdx

Select one:
a.
−12x2cos2x+12xsin2x+14cos2x+c−12x2cos2x+12xsin2x+14cos2x+c
b.
12x2cos2x−12xsin2x+14cos2x+c12x2cos2x−12xsin2x+14cos2x+c

c.
12x2cos2x+12xsin2x+14cos2x+c12x2cos2x+12xsin2x+14cos2x+c
 d.
−12x2cos2x−12xsin2x+14cos2x+c−12x2cos2x−12xsin2x+14cos2x+c
Question 6
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Evaluate  ∫x2e−xdx∫x2e−xdx

Select one:
a.
−x2e−x−2[−e−x(x+1)]+C−x2e−x−2[−e−x(x+1)]+C
b.
x2e−x−2[−e−x(x+1)]+Cx2e−x−2[−e−x(x+1)]+C
c.
x2e−x+2[−e−x(x+1)]+Cx2e−x+2[−e−x(x+1)]+C
d.
−x2e−x+2[−e−x(x+1)]+C−x2e−x+2[−e−x(x+1)]+C

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Evaluate  ∫x sin x dx∫x sin x dx

Select one:
a.
x cos x+sin x+Cx cos x+sin x+C
b.
−x cos x+sin x+C−x cos x+sin x+C
 c.
−x cos x−sin x+C−x cos x−sin x+C
d.
x cos x−sin x+Cx cos x−sin x+C

Question 8
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Evaluate  ∫exsin x dx∫exsin x dx

Select one:
a.
12ex(sin x+cos x)+C12ex(sin x+cos x)+C

b.
13ex(sin x+cos x)+C13ex(sin x+cos x)+C

c.
12ex(sin x−cos x)+C12ex(sin x−cos x)+C

d.
13ex(sin x−cos x)+C13ex(sin x−cos x)+C

Question 9
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Evaluate  ∫xcosx dx∫xcosx dx

Select one:
a.
xsinx+cosx+Cxsinx+cosx+C
 b.
xsinx−cosx+Cxsinx−cosx+C
c.
−xsinx+cosx+C−xsinx+cosx+C
d.
−xsinx−cosx+C−xsinx−cosx+C

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Evaluate  

∫(lnsin2x)(cos2x)dx ∫(lnsin2x)(cos2x)dx

Select one:
a.
12sinx.lnsin2x−12sin2x+C12sinx.lnsin2x−12sin2x+C
b.
12sin2x.lnsin2x−12sin2x+C12sin2x.lnsin2x−12sin2x+C
c.
−12sin2x.lnsin2x+12sin2x+C−12sin2x.lnsin2x+12sin2x+C
d.
12sin2x.lnsin2x+12sin2x+C

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Find the centroid of the area bounded by y = x2, y = 4, and the y axis.

Select one:
a.
x¯=34;y¯=125x¯=34;y¯=125
b.
x¯=34;y¯=145x¯=34;y¯=145
c.
x¯=14;y¯=145x¯=14;y¯=145
d.
x¯=14;y¯=125x¯=14;y¯=125

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Find the centroid of the area bounded by the parabolas x2 = - 8y and x = y2.

Select one:
a.
x¯=95;y¯=−910x¯=95;y¯=−910
b.
x¯=−95;y¯=910x¯=−95;y¯=910
c.
x¯=−95;y¯=−910x¯=−95;y¯=−910
d.
x¯=95;y¯=910x¯=95;y¯=910
Question 3
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Find the area of the region bounded by the curves y = x3 & y = 2x2

Select one:
a.
13units213units2

b.
23units223units2

c.
53units253units2

d.
43units243units2

Question 4
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Find the centroid of the area bounded by the parabola 4x - x2 = y and y = x.

Select one:
a.
x¯=32;y¯=25x¯=32;y¯=25
b.
x¯=54;y¯=115x¯=54;y¯=115
c.
x¯=52;y¯=25x¯=52;y¯=25
d.
x¯=32;y¯=125x¯=32;y¯=125
e.
x¯=52;y¯=125x¯=52;y¯=125

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Find the area bounded by the parabola y2 = 4 - x, and the y-axis.

Select one:
a.
323units2323units2

b.
316unnits2316unnits2

c.
116units2116units2

d.
332units2332units2

Question 6
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Find the centroid of the area bounded by  x2 = 4y - 8, lines  x = 0, x = 4, and the x-axis.
 

Select one:
a.
x¯=125;y¯=425x¯=125;y¯=425
 b.
x¯=125;y¯=4725x¯=125;y¯=4725
c.
x¯=25;y¯=425x¯=25;y¯=425
d.
x¯=25;y¯=4725x¯=25;y¯=4725

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Find the area bounded by the parabola y2 = 4x, the line y = 2x - 4.

Select one:
a.
units2units2

b.
273273

c.
283units2283units2

d.
253units2253units2

Question 8
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Question text
Find the centroid of the first quadrant area bounded by the parabola 4 - x 2 = y.

Select one:
 a.
x¯=14;y¯=65x¯=14;y¯=65
b.
x¯=14;y¯=85x¯=14;y¯=85
c.
x¯=34;y¯=65x¯=34;y¯=65
d.
x¯=34;y¯=85x¯=34;y¯=85

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Question text
Find the area bounded by the parabola y = 4x – x2, and the x-axis.

Select one:
a.
316units2316units2

b.
116units2116units2

c.
322units2322units2

d.
332units2332units2

Question 10
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Question text
Find the centroid of the area bounded by the parabolas x2 = y and y = 9.
Select one:
a.
x¯=0;y¯=25x¯=0;y¯=25
b.
x¯=0;y¯=175x¯=0;y¯=175
c.
x¯=0;y¯=75x¯=0;y¯=75
d.

x¯=0;y¯=275

Question 1
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∫
Evaluate  3x5+2x2−3x3 dx∫3x5+2x2−3x3dx 
Select one:
a.
2x3++3ln|x|+32x−2+c2x3++3ln⁡|x|+32x−2+c
b.
x3++2ln|x|+32x−2+cx3++2ln⁡|x|+32x−2+c
c.
2x3++2ln|x|+32x−2+c2x3++2ln⁡|x|+32x−2+c
d.
x3++3ln|x|+32x−2+cx3++3ln⁡|x|+32x−2+c
Question 2
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Question text
Evaluate   ∫sin52xcos322xdx∫sin5⁡2xcos32⁡2xdx
Select one:
a.
  −15cos522x+29cos922x−113cos1322x+c−15cos52⁡2x+29cos92⁡2x−113cos13
2⁡2x+c
b.
15cos524x+29cos924x+113cos1324x+c15cos52⁡4x+29cos92⁡4x+113cos132⁡4x+c
c.
−15cos524x+29cos924x−113cos1324x+c−15cos52⁡4x+29cos92⁡4x−113cos132⁡4x+c
d.
15cos522x+29cos922x+cos1322x+c15cos52⁡2x+29cos92⁡2x+cos132⁡2x+c

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Evaluate   ∫(ex−xe)dx∫(ex−xe)dx
Select one:
a.
ex+xe+1e+1+cex+xe+1e+1+c
b.
−ex−xe+1e+1+c−ex−xe+1e+1+c
c.
−ex+xe+1e+1+c−ex+xe+1e+1+c
d.
e −xe+1e+1+cex−xe+1e+1+c
  x

Question 4
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Evaluate   ∫4tan2θdθ∫4tan2⁡θdθ 
Select one:
a.
tanθ−4θ+ctan⁡θ−4θ+c
b.
 tanθ−θ+ctan⁡θ−θ+c
c.
4tanθ−θ+c4tan⁡θ−θ+c
d.
4tanθ−4θ+c4tan⁡θ−4θ+c
Question 5
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Evaluate   ∫e2−5xdx∫e2−5xdx
Select one:
 a.
−12−5e2−5x+c−12−5e2−5x+c
b.
−15e2−5x+c−15e2−5x+c
c.
15e2−5x+c15e2−5x+c
d.
12−5e2−5x+c12−5e2−5x+c

Question 6
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Evaluate  ∫xsin3x2dx∫xsin⁡3x2dx  
Select one:
a.
−13sin3x2+c−13sin⁡3x2+c
b.
−16sin3x2+c−16sin⁡3x2+c
c.
  −13cos3x2+c−13cos⁡3x2+c
d.
−16cos3x2+c−16cos⁡3x2+c
Question 7
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Evaluate  ∫sin4θdθ∫sin4⁡θdθ  
Select one:
a.
38θ−sin2θ4+sin4θ32+c38θ−sin⁡2θ4+sin⁡4θ32+c
b.
35θ−sin2θ4+sin4θ32+c35θ−sin⁡2θ4+sin⁡4θ32+c
c.
18θ−sin2θ4+sin4θ32+c18θ−sin⁡2θ4+sin⁡4θ32+c
d.
58θ−sin2θ4+sin4θ32+c58θ−sin⁡2θ4+sin⁡4θ32+c

Question 8
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∫
Evaluate  sec5xcscx dx∫sec5⁡xcsc⁡xdx 
Select one:
a.
∫sec5x5+c∫sec5⁡x5+c
b.
∫sec4x4+c∫sec4⁡x4+c
c.
∫sec5x4+c∫sec5⁡x4+c
d.
∫sec4x5+c∫sec4⁡x5+c
Question 9
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∫
Evaluate   csc23θdθ1−cot3θ∫csc2⁡3θdθ1−cot⁡3θ 

Select one:
a.
3ln(1−csc3θ)+c3ln⁡(1−csc⁡3θ)+c
b.
13ln(1−cot3θ)+c13ln⁡(1−cot⁡3θ)+c
c.
−13ln(1−cot2θ)+c−13ln⁡(1−cot⁡2θ)+c
d.
−3ln(1−csc3θ)+c−3ln⁡(1−csc⁡3θ)+c
Question 10
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Evaluate   ∫xsin3x2dx∫xsin⁡3x2dx
Select one:
 a.
−13cos3x2+c−13cos⁡3x2+c
b.
−16sin3x2+c−16sin⁡3x2+c
c.
−13sin3x2+c−13sin⁡3x2+c
d.
  −16cos3x2+c−16cos⁡3x2+c
Question 11
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∫
Evaluate   dx1+ex∫dx1+ex

Select one:
a.
−ln|ex+1|+c−ln⁡|ex+1|+c
b.
ln|ex+1|+cln⁡|ex+1|+c
c.
ln|e−x+1|+cln⁡|e−x+1|+c
d.
−ln|e−x+1|+c−ln⁡|e−x+1|+c
Question 12
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∫
Evaluate  dxx−−√(1+x−−√)∫dxx(1+x) 

Select one:
a.
ln(1+x−−√)+cln⁡(1+x)+c
b.
4ln(1+x−−√)+c4ln⁡(1+x)+c
c.
3ln(1+x−−√)+c3ln⁡(1+x)+c
d.
2ln(1+x−−√)+c2ln⁡(1+x)+c
Question 13
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Evaluate  ∫sin2θcos2θdθ∫sin2⁡θcos2⁡θdθ
Select one:
a.
  12θ−132sin4θ+c12θ−132sin⁡4θ+c
b.
 132 θ−132sin4θ+c132θ−132sin⁡4θ+c
c.
 14θ−132sin4θ+c14θ−132sin⁡4θ+c
d.
 18 θ−132sin4θ+c18θ−132sin⁡4θ+c
Question 14
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∫
Evaluate  sin34xcos24x dx∫sin3⁡4xcos2⁡4xdx  
Select one:
a.
1cosx−cosx+c1cos⁡x−cos⁡x+c
b.
2cosx+cosx+c2cos⁡x+cos⁡x+c
c.
1cosx+cosx+c1cos⁡x+cos⁡x+c
d.
2cosx−cosx+c2cos⁡x−cos⁡x+c

Question 15
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∫
Evaluate  dxxx6−25−−−−−√∫dxxx6−25 

Select one:
 a.
 35arcsecx35+c35arcsecx35+c
b.
 53arcsecx35+c53arcsecx35+c
c.
  15arcsecx35+c15arcsecx35+c
d.
 13 arcsecx35+c13arcsecx35+c
Question 16
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∫
Evaluate  dx3+2x2∫dx3+2x2

Select one:
a.
 36–√ arctan2–√x3–√+c36arctan⁡2x3+c
b.
16–√arctan2–√x3–√+c16arctan⁡2x3+c
c.
 66–√ arctan2–√x3–√+c66arctan⁡2x3+c
d.
 26–√ arctan2–√x3–√+c26arctan⁡2x3+c
Question 17
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∫
Evaluate  sec2x1+9tan2x dx∫sec2x1+9tan2xdx 
Select one:
a.
arctan(9tanx)+carctan(9tanx)+c
b.
13arctan(3tanx)+c13arctan(3tanx)+c
c.
arctan(3tanx)+carctan(3tanx)+c
d.
13arctan(9tanx)+c13arctan(9tanx)+c

Question 18
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Evaluate  ∫e4xdx∫e4xdx 
Select one:
a.
 4∙34xln3+c4•34xln⁡3+c
b.
14∙34xln3+c14•34xln⁡3+c
c.
13∙34xln3+c13•34xln⁡3+c
d.
34xln3+c34xln⁡3+c

Question 19
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Evaluate  ∫cot3xcot32xdx∫cot3⁡xcot32⁡xdx  
Select one:
a.
−72csc72x−23csc32x+c−72csc72⁡x−23csc32⁡x+c
b.
  −27csc72x+23csc32x+c−27csc72⁡x+23csc32⁡x+c
c.
−27csc72x−23csc32x+c−27csc72⁡x−23csc32⁡x+c
d.
−72csc72x+23csc32x+c−72csc72⁡x+23csc32⁡x+c
Question 20
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∫
Evaluate  dxx[1+ln2x]∫dxx[1+ln2x] 

Select one:
 a.
2arctan(ln2x)+c2arctan(ln2x)+c
b.
2arctan(lnx)+c2arctan(lnx)+c
c.
arctan(lnx)+carctan(lnx)+c
d.
arctan(ln2x)+carctan(ln2x)+c

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∫
Evaluate  arctanx1+x2 dx∫arctan⁡x1+x2dx 
Select one:
a.
3arctan2x2+c3arctan2⁡x2+c
b.
2arctan2x3+c2arctan2⁡x3+c
c.
 arctan2x2 +carctan2⁡x2+c
d.
arctan2x3+carctan2⁡x3+c

Question 2
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Question text
Evaluate  ∫e2xdx∫e2xdx  
Select one:
a.
12e2x+2x+c12e2x+2x+c
b.
12e2x+c12e2x+c
c.
2e2x+2x+c2e2x+2x+c
d.
2e2x+c2e2x+c
Question 3
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∫
Evaluate   sin2θ1+sin2θ dθ∫sin⁡2θ1+sin2⁡θdθ
Select one:
a.
ln|1+sin2θ|+cln⁡|1+sin2⁡θ|+c
b.
2ln|1+sin2θ|+c2ln⁡|1+sin2⁡θ|+c
c.
ln|1+2sin2θ|+cln⁡|1+2sin2⁡θ|+c
d.
2ln|1+sin2θ|+c2ln⁡|1+sin2⁡θ|+c
Question 4
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∫
Evaluate  sec2x1+9tan2x dx∫sec2x1+9tan2xdx 
Select one:
a.
arctan(3tanx)+carctan(3tanx)+c
b.
13arctan(3tanx)+c13arctan(3tanx)+c
c.
arctan(9tanx)+carctan(9tanx)+c
d.
13arctan(9tanx)+c13arctan(9tanx)+c

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∫
Evaluate  1+e2xex dx∫1+e2xexdx 
Select one:
 a.
−e−x−ex+c−e−x−ex+c
b.
  −e−x+ex+c−e−x+ex+c
c.
e−x−ex+ce−x−ex+c
d.

e−x+ex+ce−x+ex+c
Question 6
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∫
Evaluate  dxxx6−25−−−−−√∫dxxx6−25 

Select one:
a.
 35 arcsecx35+c35arcsecx35+c
b.
  15arcsecx35+c15arcsecx35+c
c.
 53 arcsecx35+c53arcsecx35+c
d.
 13 arcsecx35+c13arcsecx35+c
Question 7
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∫
Evaluate  dxx1−ln2x−−−−−−√∫dxx1−ln2⁡x  

Select one:
a.
  2arcsin(lnx)+c2arcsin⁡(lnx)+c
b.
arcsin(ln2x)+carcsin⁡(ln2⁡x)+c
c.
2arcsin(ln2x)+c2arcsin⁡(ln2⁡x)+c
d.
  arcsin(lnx)+carcsin⁡(ln⁡x)+c
Question 8
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∫
Evaluate  x−−√dx1+xx−−√∫xdx1+xx  

Select one:
a.
13ln(1+xx−−√)+c13ln⁡(1+xx)+c
b.
15ln(1+xx−−√)+c15ln⁡(1+xx)+c
c.
23ln(1+xx−−√)+c23ln⁡(1+xx)+c
d.
25ln(1+xx−−√)+c25ln⁡(1+xx)+c

Question 9
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∫
Evaluate  dxx[1+ln2x]∫dxx[1+ln2x] 

Select one:
a.
arctan(lnx)+carctan(lnx)+c
b.
2arctan(ln2x)+c2arctan(ln2x)+c
c.
arctan(ln2x)+carctan(ln2x)+c
d.
2arctan(lnx)+c2arctan(lnx)+c

Question 10
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Evaluate  ∫e4xdx∫e4xdx 
Select one:
a.
13∙34xln3+c13•34xln⁡3+c
b.
34xln3+c34xln⁡3+c
c.
 4∙34xln3+c4•34xln⁡3+c
d.
14∙34xln3+c

Question 1
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Evaluate   ∫exex−2−−−−−√dx∫exex−2dx
Select one:
a.

 25 (ex−2)3−−−−−−−√+c25(ex−2)3+c
b.

25(ex−2)5−−−−−−−√+c25(ex−2)5+c

c.

23(ex−2)5−−−−−−−√+c23(ex−2)5+c

d.

 23 (ex−2)3−−−−−−−√+c23(ex−2)3+c
Question 2
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Evaluate  ∫(t+1t)32(t2−1t2)dt∫(t+1t)32(t2−1t2)dt  
Select one:
a.
 32(t+1t)23+c32(t+1t)23+c
b.
 25 (t+1t)52+c25(t+1t)52+c
c.
 32(t+1t)52+c32(t+1t)52+c
d.
 25(t+1t)23+c25(t+1t)23+c
Question 3
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∫
Evaluate  3x5+2x2−3x3 dx∫3x5+2x2−3x3dx 
Select one:
a.
2x3++2ln|x|+32x−2+c2x3++2ln⁡|x|+32x−2+c
b.
x3++2ln|x|+32x−2+cx3++2ln⁡|x|+32x−2+c
c.
x3++3ln|x|+32x−2+cx3++3ln⁡|x|+32x−2+c
d.
2x3++3ln|x|+32x−2+c2x3++3ln⁡|x|+32x−2+c
Question 4
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Evaluate  ∫sin2θsin4θdθ∫sin⁡2θsin⁡4θdθ 
Select one:
a.
sin32θ2+csin3⁡2θ2+c
b.
sin34θ3+csin3⁡4θ3+c
c.
 sin32θ3 +csin3⁡2θ3+c
d.
sin34θ2+csin3⁡4θ2+c

Question 5
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Evaluate  ∫xsin3x2dx∫xsin⁡3x2dx  
Select one:
a.
−16sin3x2+c−16sin⁡3x2+c
b.
−16cos3x2+c−16cos⁡3x2+c
c.
  −13cos3x2+c−13cos⁡3x2+c
d.
−13sin3x2+c−13sin⁡3x2+c
Question 6
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∫
Evaluate   csc23θdθ1−cot3θ∫csc2⁡3θdθ1−cot⁡3θ 

Select one:
a.
3ln(1−csc3θ)+c3ln⁡(1−csc⁡3θ)+c
b.
−3ln(1−csc3θ)+c−3ln⁡(1−csc⁡3θ)+c
c.
−13ln(1−cot2θ)+c−13ln⁡(1−cot⁡2θ)+c
d.
13ln(1−cot3θ)+c13ln⁡(1−cot⁡3θ)+c

Question 7
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Question text
Evaluate   ∫xsin3x2dx∫xsin⁡3x2dx
Select one:
a.
−13sin3x2+c−13sin⁡3x2+c
b.
−16sin3x2+c−16sin⁡3x2+c
c.
  −16cos3x2+c−16cos⁡3x2+c
d.
−13cos3x2+c−13cos⁡3x2+c
Question 8
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∫ cosπxdx∫1x2cos⁡πxdx
Evaluate   1x2

Select one:
a.
−1πcosπx+c−1πcos⁡πx+c
b.
  −1πsinπx+c−1πsin⁡πx+c
c.
1πsinπx+c1πsin⁡πx+c
d.
1πcosπx+c1πcos⁡πx+c

Question 9
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Evaluate   ∫4tan2θdθ∫4tan2⁡θdθ 
Select one:
a.
4tanθ−θ+c4tan⁡θ−θ+c
b.
4tanθ−4θ+c4tan⁡θ−4θ+c
c.
 tanθ−θ+ctan⁡θ−θ+c
d.
tanθ−4θ+ctan⁡θ−4θ+c
Question 10
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∫
Evaluate  sin3x+cos3xdxcos3x∫sin⁡3x+cos⁡3xdxcos3x  

Select one:
 a.
13ln|csc3x|+x+c13ln⁡|csc⁡3x|+x+c
b.
12ln|sec3x|+x+c12ln⁡|sec⁡3x|+x+c
c.
13ln|sec3x|+x+c13ln⁡|sec⁡3x|+x+c
d.
13ln|sin3x|+x+c

UGRD-MATH212 Integral Calculus

1. Home
2. My courses
3. UGRD-MATH212-2033T
4. Week 14: Final Exams
5. Final Exam

Started on Tuesday, 22 June 2021, 3:16 PM

State Finished

Completed on Tuesday, 22 June 2021, 3:54 PM

Time taken 37 mins 39 secs

Marks 42.00/50.00

Grade 84.00 out of 100.00

Question 1
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 ∫
Evaluate   x−−√dx(4+x)2∫xdx(4+x)2
Select one:

a.

12θ+34sin2θ+c12θ+34sin2θ+c
b.

12θ−34sin2θ+c12θ−34sin2θ+c
c.

12θ−14sin2θ+c12θ−14sin2θ+c
d.

12θ+14sin2θ+c12θ+14sin2θ+c
Question 2
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Find the area bounded by the parabola y2 = 4x, the line y = 2x - 4.
Select one:

a.

283units2283units2

b.

273273

c.

253units2253units2
 d.

units2units2
Question 3
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∫ ∫
Evaluate   21 y3−−√0∫12∫0y3 xy2  dxdyxy2 dxdy
Select one:

a.

4343

b.

3232

c.

3434

d.

1414
Question 4
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Evaluate   ∫10∫x0∫x+y0(2x+
y−1)dzdydx∫01∫0x∫0x+y(2x+y−1)dzdydx
Select one:

a.

17241724

b.

15241524

c.

13241324

d.

11241124
Question 5
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∫ ∫
Evaluate   1−1 1−1 1−1 ∫ (x+y+z)dxdydz∫−11∫−11∫−11(x+y+z)dxdydz
Select one:

a.

b.

3
 c.

d.

Question 6
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Find the volume of the solid generated by rotating the region bounded by the given curves
and lines about the indicated axis y2 = x3, y = 0; and x = 2 about the x axis.
Select one:

a.

4π54π5

b.

4π

c.

5π45π4

d.

5π

Question 7
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Question text
Find the area of the region bounded by the curves y = x3 & y = 2x2
Select one:

a.

43units243units2

b.

53units253units2

c.

23units223units2

d.

13units213units2
Question 8
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Evaluate  ∫x2x+1dx−−−−−−−√∫x2x+1dx
Select one:

a.

z77+4z55+2z33+cz77+4z55+2z33+c

b.
2z77+4z55+2z33+c2z77+4z55+2z33+c

c.

2z77+3z55+2z33+c2z77+3z55+2z33+c

d.

2z77+4z55+z33+c2z77+4z55+z33+c
Question 9
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Find the centroid of the area bounded by the parabola 4x - x2 = y and y = x.
Select one:

a.

x¯=54;y¯=115x¯=54;y¯=115
b.

x¯=32;y¯=25x¯=32;y¯=25
c.

x¯=52;y¯=125x¯=52;y¯=125
d.

x¯=52;y¯=25x¯=52;y¯=25
e.

x¯=32;y¯=125x¯=32;y¯=125
Question 10
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Find the centroid of the area bounded by the parabola 4x - x2 = y and y = 0.
Select one:

a.

x¯=1;y¯=65x¯=1;y¯=65
b.

x¯=2;y¯=85x¯=2;y¯=85
c.

x¯=1;y¯=85x¯=1;y¯=85
d.

x¯=2;y¯=65x¯=2;y¯=65
Question 11
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Evaluate  

∫sinθcos2θ1+cosθ−−−−−−√dθ ∫sinθcos2θ1+cosθdθ

Select one:

a.
2z55+4z33−2z+c2z55+4z33−2z+c
b.

2z55−4z33−2z+c2z55−4z33−2z+c
c.

−2z55+4z33−2z+c−2z55+4z33−2z+c
d.

−2z55−4z33−2z+c−2z55−4z33−2z+c
Question 12
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Find the centroid of the first quadrant area bounded by the parabola 4 - x 2 = y.
Select one:

a.

x¯=34;y¯=85x¯=34;y¯=85
b.

x¯=34;y¯=65x¯=34;y¯=65
c.

x¯=14;y¯=85x¯=14;y¯=85
d.

x¯=14;y¯=65x¯=14;y¯=65
Question 13
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Evaluate  ∫ln(x−−√+1)dx∫ln(x+1)dx
Select one:

a.

z2ln(z+1)+z22+z−ln(z+1)+cz2ln(z+1)+z22+z−ln(z+1)+c
b.

−z2ln(z+1)+z22+z−ln(z+1)+c−z2ln(z+1)+z22+z−ln(z+1)+c
c.

z2ln(z+1)−z22+z−ln(z+1)+cz2ln(z+1)−z22+z−ln(z+1)+c
d.

−z2ln(z+1)−z22+z−ln(z+1)+c−z2ln(z+1)−z22+z−ln(z+1)+c
Question 14
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Find the volume of the solid generated by rotating the region bounded by the given curves
and lines about the indicated axis y = 2x2; x = 0; y = 0; x = 5; about the x axis.
Select one:

a.
2500π

b.

1500π

c.

2000π

d.

3000π

Question 15
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Evaluate  ∫dx16+9x2−−−−−−√ ∫dx16+9x2

Select one:

a.

13ln(secθ−tanθ)+c13ln(secθ−tanθ)+c
b.

13ln(secθ+tanθ)+c13ln(secθ+tanθ)+c
c.

23ln(secθ−tanθ)+c23ln(secθ−tanθ)+c
d.

23ln(secθ+tanθ)+c23ln(secθ+tanθ)+c
Question 16
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Evaluate  

∫(x−−√+1)14dx ∫(x+1)14dx

Select one:

a.

49(z+1)94−45(z+1)54+c49(z+1)94−45(z+1)54+c
b.

89(z+1)94−45(z+1)54+c89(z+1)94−45(z+1)54+c
c.

49(z+1)94−25(z+1)54+c49(z+1)94−25(z+1)54+c
d.

89(z+1)94−25(z+1)54+c89(z+1)94−25(z+1)54+c
Question 17
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Question text
∫ ∫
Evaluate   10 1−x0 (2−x−y)dydx∫01∫01−x(2−x−y)dydx
Select one:

a.

3232

b.

2323

c.

1313

d.

4343
Question 18
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Find the centroid of the area bounded by the parabolas x2 = - 8y and x = y2.
Select one:

a.

x¯=95;y¯=−910x¯=95;y¯=−910
b.

x¯=95;y¯=910x¯=95;y¯=910
c.

x¯=−95;y¯=−910x¯=−95;y¯=−910
d.
x¯=−95;y¯=910x¯=−95;y¯=910
Question 19
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Evaluate  ∫dxxx2−2x−−−−−√ ∫dxxx2−2x

Select one:

a.

2sin2θ+c2sin2θ+c
b.

2sinθ+c2sinθ+c
c.

sin2θ+csin2θ+c
d.

sinθ+csinθ+c
Question 20
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Find the area of the region bounded by y = x2, y = 4, and the y axis.
Select one:

a.

173units2173units2

b.

143units2143units2

c.

163units2163units2

d.

152units2152units2
Question 21
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Evaluate  

∫xx−2−−−−√dx ∫xx−2dx

Select one:

a.

2z53+z35+C2z53+z35+C
b.

z53+4z33+Cz53+4z33+C

c.
z55+z35+Cz55+z35+C
d.

2z55+4z33+C2z55+4z33+C
Question 22
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Find the centroid of the area bounded by y = x2, y = 4, and the y axis.
Select one:

a.

x¯=14;y¯=145x¯=14;y¯=145
b.

x¯=34;y¯=145x¯=34;y¯=145
c.

x¯=34;y¯=125x¯=34;y¯=125
d.

x¯=14;y¯=125x¯=14;y¯=125
Question 23
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Question text
Find the centroid of the area bounded by the parabolas x2 = y and y = 9.
Select one:

a.

x¯=0;y¯=25x¯=0;y¯=25
b.

x¯=0;y¯=175x¯=0;y¯=175
c.

x¯=0;y¯=75x¯=0;y¯=75
d.

x¯=0;y¯=275x¯=0;y¯=275
Question 24
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Find the area bounded by the parabola y2 = 4 - x, and the y-axis.
Select one:

a.

316unnits2316unnits2

b.

323units2323units2

c.

332units2332units2
 d.

116units2116units2
Question 25
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∫ ∫ ∫
Evaluate   60 12−2y0 4−2y3−x30 x dzdydx∫06∫012−2y∫04−2y3−x3x dzdydx
Select one:

a.

134

b.

146

c.

136

d.

144

Question 26
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Question text
∫
Evaluate   x2−9dx−−−−−−√x∫x2−9dxx
Select one:

a.

5tanθ−3θ+c5tanθ−3θ+c
b.

3tanθ−3θ+c3tanθ−3θ+c
c.

5tanθ+3θ+c5tanθ+3θ+c
d.

3tanθ+3θ+c3tanθ+3θ+c
Question 27
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∫ ∫
Evaluate   π0 cosθ0∫0π∫0cosθ  βsinθ dβdθβsinθ dβdθ
Select one:

a.

1313

b.

1212

c.

3232

d.
2323
Question 28
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Evaluate   ∫10∫x0∫x+y0(x+y+z) dzdydx∫01∫0x∫0x+y(x+y+z) dzdydx
Select one:

a.

924924

b.

524524

c.

324324

d.

724724
Question 29
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Evaluate  ∫dxex−1−−−−√ ∫dxex−1

Select one:
 a.

3θ+c3θ+c
b.

4θ+c4θ+c
c.

2θ+c2θ+c
d.

θ+cθ+c
Question 30
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Find the area bounded by the parabola y = 4x – x2, and the x-axis.
Select one:

a.

116units2116units2

b.

316units2316units2

c.

332units2332units2

d.

322units2