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Math 10B.
Final Examination
March 16, 2004
Read each question carefully, and answer each question completely.
Show all of your work. No credit will be given for unsupported answers.
Write your solutions clearly and legibly. No credit will be given for illegible solutions.
1. (6 points) The function
E
(
x
) is defined by
E
(
x
) =
1
2
+
1
√
2
π
x
0
e

t
2
2
dt
.
(a) Compute
E
(0).
(b) Compute
E
(0).
(c) Compute
E
(1).
#
Score
1
2
3
4
5
6
7
8
9
Σ
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2. (8 points) Compute the following definite integrals.
(a)
1
0
xe
x
2
dx
(b)
1
0
x
3
e
x
2
dx
3. (4 points) Use the Trapezoidal Rule with four subintervals (
n
= 4) to estimate
1 +
x
3
dx
.
Do not simplify the resulting expression.
4
0
1
√
4. (4 points) Determine whether
x

5
2
dx
converges, and if it does, find its value.
∞
1
5. (4 points) After conducting extensive research, the American Automobile Association
has discovered that the length of time between tuneups for minivans is a continuous
random variable
T
, measured in years, and that the probability density function for
T
is
f
(
T
) =
0
if
T <
0
1
9
Te

T
3
if
T
≥
0
What is the probability that a minivan will be driven between one and two years