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Sma 2173: Calculus Ii Question Paper

Sma 2173: Calculus Ii

Course:Bachelor Of Science In Geospatial Information Science

Institution: Dedan Kimathi University Of Technology question papers

Exam Year:2013

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DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
UNIVERSITY EXAMINATIONS 2012/2013
YEAR ONE SEMESTER TWO EXAMINATION FOR THE BACHELOR OF SCIENCE IN
ENGINEEMECHATRONIC RING,MECHANICAL ENGINEERING,GEOMATIC
ENGINEERING AND GEOSPATIAL INFORMATION SYSTEMS, GEOSPATIAL
INFORMATION SCIENCE,ELECTRICAL AND ELECTRONIC
ENGINEERING,TELECOMMUNICATION AND INFORMATION ENGINEERING, CIVIL
ENGINEERING & INDUSTRIAL CHEMISTRY
SMA 2173: CALCULUS II
DATE: 23RD APRIL 2013 TIME: 11.00AM-1.00PM
INSTRUCTIONS: Answer Question One and any other Two Questions.
Question One (30 Marks)
a) Determine the equation of the normal to the curve: 2 2 6 2 2 x ? xy ? y ? x ? y ? at
(3,2). (5 marks)
b) Show that cosh ln 1, 1 1 2 ? ? ? ? ? x x x .
Hence or otherwise find (cosh ) ?1
dx
d
. (6 marks)
c) By partial fractions evaluate: ? ?
dx
x2 1
1
(4 marks)
d) Find the volume generated when the area enclosed by the x-axis and the curve
2 3 y ? 3x ? x is rotated about the x-axis. (4 marks)
e) Sketch the curve:
2
3
?
?
?
x
x
y (5 marks)
f) Use the trapezoidal rule with n=4 to estimate ? ?
1
0
2 1
1
dx
x
.
Calculate the difference between the actual value and the estimate. (6 marks)
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Question Two (20 Marks)
a) Evaluate: (sec ) 1h x
dx
d ? , hence prove that (sec (cos )) sec . 1 h x x
dx
d
? ? (7 marks)
b) Integrate: (i) ? x (x ?1)dx (4 marks)
(ii) ?
?
dx
4x 9
1
2
(4 marks)
(iii) ?
2
0
2 3 sin cos
?
x xdx (5 marks)
Question Three (20 Marks)
a) Find y?? given that 0 2 y ? x y ? xy ? . (6 marks)
b) Solve the differential equation: (1 ) 0 2 ? ? ? ? y xe
dx
dy
x (3 marks)
c) Use Trapezoidal and Simpson’s rules to evaluate the composite function
dx
x
x
I ? ?
?
1
0 1
correct to 4d.p. with n=4.
What is the exact value of dx
x
x
I ? ?
?
1
0 1
? (11 marks)
Question Four (20 Marks)
a) Find the length of the curve: 1
3
2
2
3
x ? y ? from y=0 to y=3. (6 marks)
b) Evaluate: ?
1
0
2 3 x e dx. x (7 marks)
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c) Find the area of surface of revolution generated by revolving about y-axis the arc
3 x ? y from y=0 to y=1. (7 marks)
Question Five (20 Marks)
a) Find the area bounded by the curves 4 2 y ? x ? and 8 2 . 2 y ? ? x (5 marks)
b) Evaluate: (i) ? ?
1
0
1 x tan xdx (5 marks)
(ii) ? ? 3 2 x x
dx
(5 marks)
(iii) ? xdx 5 cos (5 marks)

Sma 2173: Calculus Ii Question Paper

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