Practice Exam 1 Solutions
Most of the multiple choice answers are (A); the following are typos:
•
The answer to 2 is 8
π
, which is (C).
•
The lamina in 3 should be Ω =
{
(
x, y
) :
x
2
+
y
2
≤
π
2
, y
≥
0
}
(NOT
x
2
+
y
2
=
π
).
The answer to this problem is (A).
•
In 7,
the volume of
is written twice; otherwise it is fine, and the answer is (A).
•
8: The integrand should be
x

2
y
. The answer to this problem is 16, which is not
listed as a choice. (Note: Even if you assume the function is
x
+ 2
y
the answer you
got is still not listed as one of the choices.)
•
In 9, the transformation should have
y
= 2
v
(NOT
y
= 3
v
) and the answer is 0, which
is not listed as one of the choices.
•
10: The answer is 30, which is not listed.
13. Evaluate the interated integral
R
3
0
R
0

√
9

y
2
x
2
y dx dy
by converting to polar coordinates.
First, we are integrating over the region
D
=
{
(
x, y
) :

p
9

y
2
≤
x
≤
0
,
0
≤
y
≤
3
}
which
corresponds to the quater of the circle of radius 3 in the second quadrent. Therefore
Z
3
0
Z
0

√
9

y
2
x
2
y dx dy
=
ZZ
D
x
2
y dA
=
Z
3
0
Z
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 Fall '11
 Staff
 SEPTA Regional Rail, dr dθ, dx dy

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