Question 1

Find the center of mass of a homogeneous solid bounded by the paraboloid  and

Accepted Answer

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Question 2

Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate  where E lies above the paraboloid  and below the plane  .
A)  160.28
B)175.37
C)176.38
D)175.93
E)

Accepted Answer

E

Question 3

Use the transformation  to evaluate the integral  , where R is the region bounded by the ellipse  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

C

Question 4

Find the mass of the solid S bounded by the paraboloid  and the plane  if S has constant density 3.
A)15.07
B)16.25
C)24.91
D)13.92
E)19.63

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Question 5

Find the Jacobian of the transformation.

Accepted Answer

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Question 6

Use cylindrical coordinates to evaluate the triple integral  where E is the solid that lies between the cylinders  and  above the xy-plane and below the plane  .
A)0.54
B)0
C)3.4
D)8.57
E)9.19

Accepted Answer

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Question 7

Use a triple integral to find the volume of the solid bounded by  and the planes  and  .
A) 
B) 
C) 
D) 
E)

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Question 8

Find the Jacobian of the transformation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the Jacobian of the transformation. 
A)...

Question 9

Use the given transformation to evaluate the integral.  , where R is the region in the first quadrant bounded by the lines  and the hyperbolas  .
A)4.447
B)3.296
C)5.088
D)9.447
E)8.841

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Question 10

Identify the surface with equation

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Question 11

Identify the surface with equation

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Question 12

Use cylindrical coordinates to evaluate  where T is the solid bounded by the cylinder  and the planes  and 
A)  
B)  
C)  
D)

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Question 13

Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.
A)  k 
B)  k 
C)  k 
D)  k

Accepted Answer

The answer of Find the mass of a solid hemisphere...

Question 14

Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places.  R is the parallelogram bounded by the lines  .

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Question 15

Calculate the iterated integral. 
A) 
B)8
C) 
D) 
E)None of these

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A) 
B)8
C) 
D)...

Question 16

Use spherical coordinates to find the volume of the solid that lies within the sphere  above the xy-plane and below the cone  . Round the answer to two decimal places.

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Question 17

Use the given transformation to evaluate the integral.  , where R is the square with vertices (0, 0), (4, 6), (6,  ), (10, 2) and 
A)208
B)42
C)312
D)52
E)343

Accepted Answer

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Question 18

Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius  and density 1 about a diameter of its base.
A)195.22
B) 
C)205.13
D)198.08
E)213.5

Accepted Answer

The answer of Use spherical coordinates to find the moment...

Question 19

Use spherical coordinates.Evaluate  , where  is the ball with center the origin and radius  .
A) 
B) 
C) 
D) 
E)None of these

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Question 20

Use cylindrical coordinates to evaluate 
A)  
B)  
C)  
D)

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A) ...

Quiz 12: Multiple Integrals

Find the center of mass of a homogeneous solid bounded by the paraboloid and

Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane .

Use the transformation to evaluate the integral , where R is the region bounded by the ellipse .

Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.

Find the Jacobian of the transformation.

Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane .

Use a triple integral to find the volume of the solid bounded by and the planes and .

Find the Jacobian of the transformation.

Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas .

Identify the surface with equation

Identify the surface with equation

Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and

Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.

Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places. R is the parallelogram bounded by the lines .

Calculate the iterated integral.

Use spherical coordinates to find the volume of the solid that lies within the sphere above the xy-plane and below the cone . Round the answer to two decimal places.

Use the given transformation to evaluate the integral. , where R is the square with vertices (0, 0) , (4, 6) , (6, ) , (10, 2) and

Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius and density 1 about a diameter of its base.

Use spherical coordinates.Evaluate , where is the ball with center the origin and radius .

Use cylindrical coordinates to evaluate