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Deck 14: Section 6: Multiple Integration
Full screen (f)
Question
Find the center of mass of the solid bounded by 
and 
with density function 
.
A)
B)
C)
D)
E)
and with density function .A)
B)
C)
D)
E)
Question
Evaluate the iterated integral 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find 
of the center of mass of the solid of given density 
bounded by the graphs of the equations 
.
A)
B)
C)
D)
E)
of the center of mass of the solid of given density bounded by the graphs of the equations .A)
B)
C)
D)
E)
Question
Find the average value of 
over the region Q, where Q is a cube in the first octant bounded by the coordinate planes, and the planes 
and 
. The average value of a continuous function 
over a solid region Q is 
, where V is the volume of the solid region Q.
A)
B)
C)
D)
E)
over the region Q, where Q is a cube in the first octant bounded by the coordinate planes, and the planes and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.A)
B)
C)
D)
E)
Question
Find the centroid of the solid region bounded by the graphs of the equations. Use a computer algebra system to evaluate the triple integral. (Assume uniform density and find the center of mass.) 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the average value of 
over the region Q, where Q is a tetrahedron in the first octant with vertices 
and 
. The average value of a continuous function 
over a solid region Q is 
, where V is the volume of the solid region Q.
A)
B)
C)
D)
E)
over the region Q, where Q is a tetrahedron in the first octant with vertices and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.A)
B)
C)
D)
E)
Question
Use a triple integral to find the volume of the solid bounded by the graphs of the equations 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the following iterated integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
for the indicated solid with density function 
. 
A)
B)
C)
D)
E)
for the indicated solid with density function . A)
B)
C)
D)
E)
Question
Evaluate the following iterated integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Set up a triple integral for the volume of the solid bounded above by the cylinder 
and below by the paraboloid 
.
A)
B)
C)
D)
E)
and below by the paraboloid .A)
B)
C)
D)
E)
Question
Determine the value of b so that the volume of the ellipsoid 
is 
.
A)
B)
C)
D)
E)
is .A)
B)
C)
D)
E)
Question
Set up a triple integral that gives the moment of inertia about the 
-axis of the solid region Q of density given below. 
A)
B)
C)
D)
E)
-axis of the solid region Q of density given below. A)
B)
C)
D)
E)
Question
Use a triple integral to find the volume of the solid shown below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a triple integral to find the volume of the solid shown below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Rewrite the iterated integral 
using the order 
.
A)
B)
C)
D)
E)
using the order .A)
B)
C)
D)
E)
Question
Set up a triple integral for the volume of the solid bounded by 
and 
.
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
Question
Sketch the solid whose volume is given by the iterated integral given below and use the sketch to rewrite the integral using the indicated order of integration. 
Rewrite the integral using the order 
.
A)
B)
C)
D)
E)
Rewrite the integral using the order .A)
B)
C)
D)
E)
Question
Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 14: Section 6: Multiple Integration
1
Find the center of mass of the solid bounded by and with density function .
A)
B)
C)
D)
E)
and with density function .A)
B)
C)
D)
E)
2
Evaluate the iterated integral .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
3
Find of the center of mass of the solid of given density bounded by the graphs of the equations .
A)
B)
C)
D)
E)
of the center of mass of the solid of given density bounded by the graphs of the equations .A)
B)
C)
D)
E)
4
Find the average value of over the region Q, where Q is a cube in the first octant bounded by the coordinate planes, and the planes and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.
A)
B)
C)
D)
E)
over the region Q, where Q is a cube in the first octant bounded by the coordinate planes, and the planes and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.A)
B)
C)
D)
E)
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5
Find the centroid of the solid region bounded by the graphs of the equations. Use a computer algebra system to evaluate the triple integral. (Assume uniform density and find the center of mass.)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Find the average value of over the region Q, where Q is a tetrahedron in the first octant with vertices and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.
A)
B)
C)
D)
E)
over the region Q, where Q is a tetrahedron in the first octant with vertices and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 19 flashcards in this deck.
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7
Use a triple integral to find the volume of the solid bounded by the graphs of the equations .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock for access to all 19 flashcards in this deck.
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8
Evaluate the following iterated integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Find for the indicated solid with density function .
A)
B)
C)
D)
E)
for the indicated solid with density function . A)
B)
C)
D)
E)
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10
Evaluate the following iterated integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 19 flashcards in this deck.
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11
Set up a triple integral for the volume of the solid bounded above by the cylinder and below by the paraboloid .
A)
B)
C)
D)
E)
and below by the paraboloid .A)
B)
C)
D)
E)
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Unlock Deck
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12
Determine the value of b so that the volume of the ellipsoid is .
A)
B)
C)
D)
E)
is .A)
B)
C)
D)
E)
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Unlock for access to all 19 flashcards in this deck.
Unlock Deck
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13
Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below.
A)
B)
C)
D)
E)
-axis of the solid region Q of density given below. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 19 flashcards in this deck.
Unlock Deck
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14
Use a triple integral to find the volume of the solid shown below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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15
Use a triple integral to find the volume of the solid shown below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 19 flashcards in this deck.
Unlock Deck
k this deck
16
Rewrite the iterated integral using the order .
A)
B)
C)
D)
E)
using the order .A)
B)
C)
D)
E)
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Unlock for access to all 19 flashcards in this deck.
Unlock Deck
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17
Set up a triple integral for the volume of the solid bounded by and .
A)
B)
C)
D)
E)
and .A)
B)
C)
D)
E)
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Unlock Deck
k this deck
18
Sketch the solid whose volume is given by the iterated integral given below and use the sketch to rewrite the integral using the indicated order of integration. Rewrite the integral using the order .
A)
B)
C)
D)
E)
Rewrite the integral using the order .A)
B)
C)
D)
E)
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19
Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 19 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 19 flashcards in this deck.
