Name:
April 2006
Mathematics 101
Page 2 of 11 pages
Marks
[33]
1.
ShortAnswer Questions.
Put your answer in the box provided but show your work also.
Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will
be given for a correct answer placed in the box, but at most one mark will be given for an
incorrect answer. Unless otherwise stated, simplify your answer as much as possible.
(a)
Find the average value of cos
x
on the interval [0
, π
].
Answer
(b)
Evaluate
cos
2
x dx
.
Answer
(c)
Evaluate
1
√
1
−
x
2
+ 1
−
x
2
dx
.
Answer
Continued on page 3
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Name:
April 2006
Mathematics 101
Page 3 of 11 pages
(d)
Write down the Simpson’s Rule approximation
S
6
for
8
2
1
x
2
dx
.
You may leave your
answer expressed as a sum of fractions.
Answer
(e)
Calculate the volume of the solid obtained by rotating the region above the
x
axis, below
the curve
y
=
x
+
x
2
, and between the lines
x
= 1 and
x
= 2 about the
x
axis.
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 Spring '10
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