Calculus II Midterm 1
February, 2009
2
1. (3 marks each; total 9 marks)
Answer each question in the space provided.
You
MUST show your work.
a)
Evaluate
∫
∞
+
1
1
dx
x
x
.
b)
Consider the integral
∫
4
2
ln
xdx
.
If using the Trapezoidal rule to approximate
this integral, the error is approximated by
2
3
12
)
(
n
a
b
K
E
T
−
≤
with
K
x
f
≤
)
(
)
2
(
.
Find the value of
K
.
[Note:
Just find
K
; you do NOT have to
approximate the resulting error]
c)
Evaluate
∫
π
0
3
cos
sin
xdx
x
.

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