Question 1

Select the correct Answer for each question.
-Find the volume of the solid bounded by the surface   and the planes   and coordinate planes.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Find the mass and the center of mass of the lamina occupying the region R, where R is the region bounded by the graphs of   and having the mass density

Accepted Answer

The answer of Find the mass and the center of...

Question 3

Evaluate the double integral by first identifying it as the volume of a solid.Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

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.Select the correct Answer

Accepted Answer

A) 205.13 
B)    
C) 195.22 
D) 213.5 
E) 198.08 
A) 205.13 
B)    
C) 195.22 
D) 213.5 
E) 198.08

Question 5

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices   and having the mass density

Accepted Answer

The answer of Find the mass and the center of...

Question 6

Evaluate the iterated integral.Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Select the correct Answer for each question.
-Calculate the iterated integral.Round yourAnswer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the area of the surface.The part of the sphere   that lies above the plane

Accepted Answer

The answer of Find the area of the surface.The part...

Question 9

Estimate the volume of the solid that lies above the square   and below the elliptic paraboloid   Divide   into four equal squares and use the Midpoint rule.

Accepted Answer

The answer of Estimate the volume of the solid that...

Question 10

Evaluate the integral by reversing the order of integration.

Accepted Answer

The answer of Evaluate the integral by reversing the order...

Question 11

Find the area of the surface.The part of the sphere   that lies above the plane

Accepted Answer

The answer of Find the area of the surface.The part...

Question 12

Select the correct Answer for each question.
-Use a computer algebra system to find the moment of inertia   of the lamina that occupies the region D and has the density function

Accepted Answer

A) 14.1 
B) 34.138 
C) 24.105 
D) 28.5 
E) None of these 
A) 14.1 
B) 34.138 
C) 24.105 
D) 28.5 
E) None of these

Question 13

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

Accepted Answer

The answer of Find the mass of the solid S...

Question 14

Select the correct Answer for each question.
-Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate   where E lies above the paraboloid   and below the plane

Accepted Answer

A)      
B)    
C)    
D)    
E)    
A)      
B)    
C)    
D)    
E)

Question 15

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.

Accepted Answer

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

Question 16

Select the correct Answer for each question.
-Find the Jacobian of the transformation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Select the correct Answer for each question.
-Evaluate the iterated integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Evaluate the integral   where R is the annular region bounded by the circles   by changing to polar coordinates.

Accepted Answer

The answer of Evaluate the integral   where R...

Question 19

Select the correct Answer for each question.
-Use polar coordinates to find the volume of the solid inside the cylinder   and the ellipsoid

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices   and having the mass density

Accepted Answer

The answer of Find the mass and the center of...

Select the correct Answer for each question. -Find the volume of the solid bounded by the surface and the planes and coordinate planes.

Find the mass and the center of mass of the lamina occupying the region R, where R is the region bounded by the graphs of and having the mass density

Evaluate the double integral by first identifying it as the volume of a solid.Select the correct Answer

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.Select the correct Answer

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and having the mass density

Evaluate the iterated integral.Select the correct Answer

Select the correct Answer for each question. -Calculate the iterated integral.Round yourAnswer to two decimal places.

Find the area of the surface.The part of the sphere that lies above the plane

Estimate the volume of the solid that lies above the square and below the elliptic paraboloid Divide into four equal squares and use the Midpoint rule.

Evaluate the integral by reversing the order of integration.

Find the area of the surface.The part of the sphere that lies above the plane

Select the correct Answer for each question. -Use a computer algebra system to find the moment of inertia of the lamina that occupies the region D and has the density function

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

Select the correct Answer for each question. -Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane

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.

Select the correct Answer for each question. -Find the Jacobian of the transformation.

Select the correct Answer for each question. -Evaluate the iterated integral.

Evaluate the integral where R is the annular region bounded by the circles by changing to polar coordinates.

Select the correct Answer for each question. -Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and having the mass density

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Vector Calculus

Second-Order Differential Equations

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Exam 15: Multiple Integrals

Select the correct Answer for each question. -Find the volume of the solid bounded by the surface and the planes and coordinate planes.

Find the mass and the center of mass of the lamina occupying the region R, where R is the region bounded by the graphs of and having the mass density

Evaluate the double integral by first identifying it as the volume of a solid.Select the correct Answer

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.Select the correct Answer

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and having the mass density

Evaluate the iterated integral.Select the correct Answer

Select the correct Answer for each question. -Calculate the iterated integral.Round yourAnswer to two decimal places.

Find the area of the surface.The part of the sphere that lies above the plane

Estimate the volume of the solid that lies above the square and below the elliptic paraboloid Divide into four equal squares and use the Midpoint rule.

Evaluate the integral by reversing the order of integration.

Find the area of the surface.The part of the sphere that lies above the plane

Select the correct Answer for each question. -Use a computer algebra system to find the moment of inertia of the lamina that occupies the region D and has the density function

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

Select the correct Answer for each question. -Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane

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.

Select the correct Answer for each question. -Find the Jacobian of the transformation.

Select the correct Answer for each question. -Evaluate the iterated integral.

Evaluate the integral where R is the annular region bounded by the circles by changing to polar coordinates.

Select the correct Answer for each question. -Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and having the mass density

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Vector Calculus

Second-Order Differential Equations

Filters