Multivariable Calculus Quiz
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MULTIPLE INTEGRALS
Question 1
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Evaluate the integral
∭
E
(
x
2
+
y
2
+
z
2
)
−
3
/
2
d
V
\iiint_E (x^2+y^2+z^2)^{-3/2} \, dV
∭
E
(
x
2
+
y
2
+
z
2
)
−
3/2
d
V
, where
E
E
E
is the solid region between the spheres of radius
a
a
a
and
b
b
b
centered at the origin, with
0
<
a
<
b
0 < a < b
0
<
a
<
b
.
A
4
π
ln
(
b
/
a
)
4\pi \ln(b/a)
4
π
ln
(
b
/
a
)
B
2
π
(
b
−
a
)
2\pi (b-a)
2
π
(
b
−
a
)
C
4
π
(
1
/
a
−
1
/
b
)
4\pi (1/a - 1/b)
4
π
(
1/
a
−
1/
b
)
D
4
π
3
(
b
3
−
a
3
)
\frac{4\pi}{3} (b^3 - a^3)
3
4
π
(
b
3
−
a
3
)
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