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Math 104 Calculus Ii Question Paper

Math 104 Calculus Ii 

Course:Bachelor Of Computing Information Systems

Institution: Kenya Methodist University question papers

Exam Year:2012



KENYA METHODIST UNIVERSITY
DEPARTMENT OF COMPUTER SCIENCE
MATH 104 CALCULUS II

Question One
a) Evaluate the following
i. ? ?
1 5
0
? x 1? x (2 marks)
ii.
5
1
? 2x ?1dx (3 marks)
b) The acceleration of a particle is given by 2 a ? 3t ?1, find the velocity given given that at
t ? 0, v ? 5m s . (3 marks)
c) Find the volume of the solid obtained by rotating about the x-axis the region under the curve
y ? 2x from x ? 0 to x ? 5. (4 marks)
d) Find the area bounded by the curve 2 y ? x and the line y ? 4 (3 marks)
e) Solve the following differential equations
i. 2 5, given 2 when 1
dy
x x y x
dx
? ?
? ? ? ? ? ?
? ?
(5 marks)
ii. 3 2 4
dz
t t
dt
? ? (5 marks)
f) Using suitable substitutions find,
i.
? ? 2 3 1
2
x
xe dx
?
? (4 marks)
ii. 2
1
1 4
dx
? x ? (4 marks)
Question two
a) Sketch the curve 3 2 y ? x ?12x ?36x hence find the area bounded by the the x-axis, and the lines
x ? 0 and x ? 6 . (10 marks)
b) Express 2
3 4
5 6
x
x x
?
? ?
in partial fraction, hence find 2
3 4
5 6
x
dx
x x
?
? ? ? (7 marks)
c) Evaluate
6
2
1
2 1
dx
x ? ? using
i. Integration
ii. Trapezoidal rule
iii. Mid – ordinate rule
iv. Simpson’s rule
In each of the approximate methods use 8 intervals and give the answers correct to 3
decimal places. (10 marks)




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