MOHIT SINGLA
Ex. Sr. Faculty BANSAL CLASSES Kota
LEVEL-I (C.W) 10. The area bounded by the ellipse 3x 2 2 y 2 6
with the co-ordinate axes in sq. units is
AREAS OF PLANE REGIONS 1. 6 2. 8 3. 12 4. 3
UNDER SIMPLE CURVES 11. The area bounded by the parabola y 2 4 x and
1. The area of region 2 x 3 y 4 0 between its latusrectum in sq units is
coordinate axes is 8 3 1
1. 2. 3. 12 4.
16 8 9 32 3 8 3
1) 2) 3) 4)
3 3 4 3 12. The area bounded by the curve y 2 x and
2. The area of the parallelogram formed by the the line x=4 in sq units is
lines 4 y 3x a 0 , 3y 4x a 0 ,
32 16 8 4
4 y 3 x 3a 0 , 3 y 4 x 2 a 0 is 1. 2. 3. 4.
3 3 3 3
1) a 2 / 5 2) a 2 / 7
13. The area bounded by the two curves y x
3) 2a 2 / 7 4) 2a 2 / 9
3. Area bounded by y={x},{.} is fractional part and x y in sq units is
of function and x = 1 is in sq.units
1 2 1 1
1. 1 2.2 3. 3 4. 4 1. 2. 3. 4.
4. The area (in square units) of the region 3 3 5 7
bounded by the curves 2 x y 2 1 and x 0 is 14. The area enclosed between the curves y ax 2
1 2 and x ay 2 a 0 is 1 sq.unit. then a =
1) 2) 3) 1 4) 2
3 3 1 2 4
5. The area bounded by tangent,normal and 1) 2) 3) 4) 3
3 3 3
x-axis at P(2,4) to the curve y x 2 is 15. The area of the region between the curves
1. 34 2. 32 3. 36 4. 24
y x 2 and y x3 in sq units is
6. The area bounded by the X-axis and the
curve y 4 x x 2 3 in sq. units is 1 1 1 1
1. 2. 3. 4.
1. 1/3 2. 2/3 3. 4/3 4. 7/3 12 3 4 2
7. The area of the region between the curve 16. The area of the region bounded by
y 4 x 2 and the line y 6 x 2 is in sq units is y x, y x 3 in sq units is
1 1 3 1 1 1 1 1
1. 2. 3. 4. 1. 2. 3. 4.
9 12 2 5 4 12 3 2
17. The area bounded by the curve y cos x , x-
8. The area bounded by the parabola x y 2 and
axis between the ordinates x 0, x 2 is
the line y x 6 is in sq units is
1. 1 sq. unit 2. 4 sq. units
125 125 125 115 2
1. 2. 3. 4. 3. sq. units 4. 2 sq. units
3 6 4 3 3
9. The area bounded by y 2 4ax and y mx is 18. The area bounded by the curves
y sin x, y cos x and the y-axis and the first
a2
sq. units then m= point of intersection in sq units is
3
1. 1 2. 2 3. 3 4. 4 1. 2 2. 2 1 3. 2 2 4. 0
19. Area bounded by f(x)= max.(sinx,cosx)
SCO-31-P, SECTOR – 17, HUDA, YAMUNA NAGAR
VIDYABHWAN, MAHAVIR COMPLEX SCO 38 GROUND FLOOR BEHIND HERITAGE HOTEL PIPLI ROAD KKR. 9992470665
MOHIT SINGLA
Ex. Sr. Faculty BANSAL CLASSES Kota
Area
c1 d1 c2 d2
2.
0 x 2 and the co-ordinate axis is equal a1b2 a2b1
to 3. Required area =
1 1 1
1.
1
sq.units 2. 2 sq.units
xdx 2 x x dx 2 xdx 1sq.unit
1
2 0 0
b 4ac
2 3/ 2
3. 2 sq.units 4. 1 sq. unit
4. Area
20. The area of the region bounded by the curves 6a 2
2x y12 1
y cos x and y 1 in sq units is 5. Area m
2 m
1) 2 2) 2 3) 3 4) 4 b 2
4ac
3/ 2
2 2 2 2 6. Area
x y 6a 2
21. The area bounded by 1 , where a 0
b 4ac
3/ 2
a b 2
and b 0 is 7. y 4x2 6x 2 ; Area
6a 2
1
b 4ac
2 3/ 2
1) ab 2) ab 3) 2ab 4) 4ab
2 8. Area
6a 2
22. The area of the region bounded by the curves 8a 2 a 2
9.
x 2 y 2 4 and y x in sq units is 3m3 3
10. Area ab
1) 2) 2 3) 2 4) 3
8a 2
11. Area
23. The area bounded by the curve y c 2 x 2 , y- 3
4
axis and the lines y = a, y = b in sq units is 12. Area 2 x dx
0
2 3/ 2 3 3/ 2
1) b a 3/2 2) b a 3/2 16a 2
3c 3c 13. Area
3 3/2 3 3
3)
4c
b a 3/ 2 4)
4c
b3/2 a3/2 1602 1
24. The area of the region formed by the curve 14. Area =
3 3
x y 4 between co-ordinate axes
x x dx
1
15. Area
2 3
0
4 8 16 5
1) 2) 3) 4) 1
3 3 3 3
16. A rea 2 x x dx
3
LEVEL-I (C.W.) - KEY 0
2n
1. 1 2.3 3.1 4.2 5. 1 6.3 17. Area or A 20 cos x dx
7.2 8.2 9.2 10.1 11.1 12.1 a
13.1 14.1 15.1 16.4 17.2 18.2 /4
19.2 20.1 21.3 22.3 23.1 24.2 18. Area cos x sin x dx
0
LEVEL-I (C.W.) - HINTS
19. f(x)= cosx 0 x / 4 = sinx x
2
2c 4 2
1. Area
ab
SCO-31-P, SECTOR – 17, HUDA, YAMUNA NAGAR
VIDYABHWAN, MAHAVIR COMPLEX SCO 38 GROUND FLOOR BEHIND HERITAGE HOTEL PIPLI ROAD KKR. 9992470665
MOHIT SINGLA
Ex. Sr. Faculty BANSAL CLASSES Kota
/4
Required area = cos x dx sin x dx (or)
0
2
4
/4
A 2 cos xdx symmetric
0
2
2x
20. Area 2 cos x 1 dx
0
1
21. Area = 4 ab 2ab
2
1
22. Reg area 2 2 sq units
2
2
b b
1 2 3/2 b
23. Reg area = x dx c y dy
3c
y a
a a
2 3/ 2
3c
b a 3/2
a2
24. Area
6
SCO-31-P, SECTOR – 17, HUDA, YAMUNA NAGAR
VIDYABHWAN, MAHAVIR COMPLEX SCO 38 GROUND FLOOR BEHIND HERITAGE HOTEL PIPLI ROAD KKR. 9992470665
