KENY A TT A UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
INSTITUTIONAL BASED PROGRAMME
EXAMINATION FOR THE DEGREE OF BACHELOR OF EDUCATION
DATE: Wednesday 1st September 2010 TIME: 8.00a.m - 10.00a.m
INSTRUCTIONS:
Answer question ONE and any other TWO.
Q1. - [Compulsory - 30 marks]
(a) Find the following indefinite integrals: (3 marks each)
1. J x~ 1dx
ii. JJ x3 +3
X2 dx
(b) Evaluate the following definite integrals: (3 marks)
:.22' d
i. 1
0
~
VI +
x
4X2
ll. 12 x2(lnx)dx.
4
1ll.1 ~dX.
o 2x + 1
(c) Find the area bounded by the graph y = 2X2 - 3x + 2, the x-axis
and the ordinates x=U, X= 2. (3 marks)
(d) Find the area of the surface swept out when the curve y = Vx
between x = 1 and x = 4 rotates about the x-axis. (3 marks)
(e) Find the volume of the solid generated by revolving the region
bounded by the graph f (x) = J sin x for 0 ::; x ::; IT and y=O
about the x-axis, (4 marks)
1
UNIVERSITY EXAMINATIONS 2009/2010
INSTITUTIONAL BASED PROGRAMME
EXAMINATION FOR THE DEGREE OF BACHELOR OF EDUCATION
DATE: Wednesday 1st September 2010 TIME: 8.00a.m - 10.00a.m
INSTRUCTIONS:
Answer question ONE and any other TWO.
Q1. - [Compulsory - 30 marks]
(a) Find the following indefinite integrals: (3 marks each)
1. J x~ 1dx
ii. JJ x3 +3
X2 dx
(b) Evaluate the following definite integrals: (3 marks)
:.22' d
i. 1
0
~
VI +
x
4X2
ll. 12 x2(lnx)dx.
4
1ll.1 ~dX.
o 2x + 1
(c) Find the area bounded by the graph y = 2X2 - 3x + 2, the x-axis
and the ordinates x=U, X= 2. (3 marks)
(d) Find the area of the surface swept out when the curve y = Vx
between x = 1 and x = 4 rotates about the x-axis. (3 marks)
(e) Find the volume of the solid generated by revolving the region
bounded by the graph f (x) = J sin x for 0 ::; x ::; IT and y=O
about the x-axis, (4 marks)
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