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Set 103: Mathematics For Engineers Question Paper

Set 103: Mathematics For Engineers

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2008

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2008/2009
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF SCIENCE
SET 103: MATHEMATICS FOR ENGINEERS
DATE: FRIDAY, 28TH DECEMBER 2008 TIME: 11.00 A.M. – 1.00 P.M.
INSTRUCTIONS: ANSWER ANY THREE QUESTIONS.
QUESTION ONE (20 MARKS)
a) Evaluate the following integrals
i) ? ? x dx 1 sin (5 marks)
ii) dx
x
x x dx
?
?
?
8
3 1 4
1
sin
(6 marks)
b) The estimated rate at which oil will be produced from a certain well t years
after production has begun is given by
t R t e 0.1 ( ) 100 ? ? barrels per year.
Find an expression that describes the total production of the oil at the end of
year t and estimate the quantity produced at the end of the third year. (9 marks)
QUESTION TWO (20 MARKS)
(a) Evaluate the integral
x x dx 2 4 ?cos sin (8 marks)
(b) Find the area generated when the curve x ? a(? ?sin? ), y ? (1?cos? )
between ? ? 0 and ? ?? , rotates about the x-axis through a complete
revolution. (12 marks)
2
QUESTION THREE
a) Evaluate the integral
? ? ?
? ?
dx
x x
x x
2 9 4
4 26 5
2
2
(8 marks)
b) i) Find the volume generated when the plane figure bounded by
y ? 5cos2x, the x-axis and the ordinates x = 0 and 2
? rotates
about the x-axis through a complete revolution. (6 marks)
ii) Use the summation concept of integration to determine the area
enclosed by the curve 2 y ? 25 ? x and the straight line y ? x ?13 (6 marks)
QUESTION FOUR (20 MARKS)
(a) Determine the integral
? ? ? 2 6 6x 5x
dx
(6 marks)
(b) A particle moves in a straight line and its acceleration after t seconds is
t 2 cos .
(i) Determine expressions for its velocity vms-1 and its displacement
x meters after t seconds, given that t = 0, the velocity is 2ms-1 and
displacement is –4 meters. (10 marks)
(ii) Determine the displacement after 3
? seconds. (4 marks)
QUESTION FIVE (20 MARKS)
(a) Using the concept of multiple integrals, find the volume of the solid enclosed
by the plane z = 0, the plane x = 1, x = 4, y = 2, y = 5 and the surface z = x + y.
Show the development of the problem concept. (10 marks)
(b) By use of Simpson’s rule with 8 intervals evaluate
? ? x dx
1.0
0.2
3 1 . (10 marks)
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Set 103: Mathematics For Engineers Question Paper

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