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SMA B201 - Adenyah (500) .

The document announces a Calculus II exam for various Bachelor of Science programs to take place on December 3rd, 2021. The exam will last 2 hours and contain 4 questions to answer. Question 1 contains 5 parts evaluating integrals using techniques like integration by parts, finding volumes of revolution, and finding areas. Questions 2 and 3 contain additional integral evaluation problems using techniques like the Trapezoidal Rule, Simpson's Rule, and trigonometric substitution. Question 4 also evaluates integrals using techniques like trigonometric substitution and half angle identities.

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Munialo George
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118 views2 pages

SMA B201 - Adenyah (500) .

The document announces a Calculus II exam for various Bachelor of Science programs to take place on December 3rd, 2021. The exam will last 2 hours and contain 4 questions to answer. Question 1 contains 5 parts evaluating integrals using techniques like integration by parts, finding volumes of revolution, and finding areas. Questions 2 and 3 contain additional integral evaluation problems using techniques like the Trapezoidal Rule, Simpson's Rule, and trigonometric substitution. Question 4 also evaluates integrals using techniques like trigonometric substitution and half angle identities.

Uploaded by

Munialo George
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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UNIVERSITY EXAMINATIONS 2021/2022 ACADEMIC YEAR

2ND YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF


SCIENCE AND BACHELOR OF EDUCATION (SCIENCE), BSC
TELCOMM, BSC COMPUTER SCI,BSC INDUSTRIAL CHEMISTRY,
BSC. PHYSICS

COURSE CODE/TITLE: SMA B201: CALCULUS II

END OF SEMESTER: I DURATION: 2 HRS


DAY/TIME:FRIDAY 9.00AM-11.00AM DATE:3/12/2021-LIB.FE1a/1b
INSTRUCTIONS: Answer question one and any other two questions

QUESTION ONE


a) Evaluate sin 2 x cos5 xdx (6 marks)
1


b) Use integration by parts to solve xe2 x dx
0
(6 marks)

1
c) Solve x 2
 5x  6
dx (6 marks)

d) Find the volume of solid formed by revolving the region bounded by washers of radius
R  3  x2 and inner radius r  3  x on the axis of the interval (0,1) (6 marks)
e) Obtain the area of the region bounded by the function f ( x)  4 x  x 2 and the x axis (6 marks)

QUESTION TWO

a) Find the arc length from the point ( x1 , y1 ) to ( x2 , y2 ) on the graph of f ( x)  mx  b (8 marks)
1
b) Use Trapezoidal rule to approximate the definite integral A  
0
x  1dx ( 7 marks)

c) Evaluate x 2 x  1 dx (5 marks)

QUESTION THREE

x
2
a) Evaluate sin xdx (7 marks)

Page 1 of 2
2
dx
b) Use Simpsons rule with n  10 to approximate the integral 
1 x
. Obtain the exact value to the

integral and find the error involved. Work to 7 points of decimal. (8 marks)
c) Find the volume of the solid formed by revolving the region bounded by the graphs y  x and
y  x about the x axis
2
(5 marks)

QUESTION FOUR

a) Use trigonometric substitution to solve  4  x 2 dx (8 marks)

 xe
4  x2
b) Evaluate dx (4 marks)


c) Using half angle identities, evaluate sin 2 x cos4 xdx (8 marks)

Page 2 of 2

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