Question 1

Use polar coordinates to find the volume of the solid bounded by the paraboloid   and the plane   .

Accepted Answer

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

Question 2

For which of the following regions would you use rectangular coordinates?

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 3

Evaluate the iterated integral.

Accepted Answer

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

Question 4

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

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

Question 5

Use the Midpoint Rule with four squares of equal size to estimate the double integral.

Accepted Answer

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

Question 6

Find the mass and the moments of inertia     and   and the radii of gyration   and   for the lamina occupying the region R, where R is the region bounded by the graphs of the equations     and   and having the mass density

Accepted Answer

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

Question 7

Calculate the iterated integral.

Accepted Answer

The answer of Calculate the iterated integral.  ...

Question 8

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

Accepted Answer

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

Question 9

Sketch the solid whose volume is given by the integral   Evaluate the integral.

Accepted Answer

The answer of Sketch the solid whose volume is given...

Question 10

Use cylindrical coordinates to evaluate   where E is the region that lies inside the cylinder   and between the planes   . Round the answer to two decimal places.

Accepted Answer

A)    
B) 2218.41 
C) 2931.90 
D) 2431.90 
E) 2818.41 
A)    
B) 2218.41 
C) 2931.90 
D) 2431.90 
E) 2818.41

Question 11

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

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 12

Evaluate   where   and T is the region bounded by the paraboloid   and the plane

Accepted Answer

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

Question 13

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 14

Use polar coordinates to evaluate.

Accepted Answer

The answer of Use polar coordinates to evaluate.  ...

Question 15

Find the mass and the moments of inertia     and   and the radii of gyration   and   for the lamina occupying the region R, where R is the rectangular region with vertices       and   , and having uniform density

Accepted Answer

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

Question 16

Find an approximation for the integral.   Use a double Riemann sum with   and the sample point in the upper right corner to
approximate the double integral, where   .

Accepted Answer

The answer of Find an approximation for the integral. ...

Question 17

Use polar coordinates to find the volume of the solid under the paraboloid   and above the disk   .

Accepted Answer

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

Question 18

Evaluate the iterated integral

Accepted Answer

The answer of Evaluate the iterated integral  ...

Question 19

Identify the surface with equation

Accepted Answer

Upper half of a righ

Question 20

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

A)    k   
B)    k   
C)    k   
D)    k   
A)    k   
B)    k   
C)    k   
D)    k

Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane .

For which of the following regions would you use rectangular coordinates?

Evaluate the iterated integral.

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.

Use the Midpoint Rule with four squares of equal size to estimate the double integral.

Find the mass and the moments of inertia and and the radii of gyration and for the lamina occupying the region R, where R is the region bounded by the graphs of the equations and and having the mass density

Calculate the iterated integral.

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

Sketch the solid whose volume is given by the integral Evaluate the integral.

Use cylindrical coordinates to evaluate where E is the region that lies inside the cylinder and between the planes . Round the answer to two decimal places.

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

Evaluate where and T is the region bounded by the paraboloid and the plane

Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid .

Use polar coordinates to evaluate.

Find the mass and the moments of inertia and and the radii of gyration and for the lamina occupying the region R, where R is the rectangular region with vertices and , and having uniform density

Find an approximation for the integral. Use a double Riemann sum with and the sample point in the upper right corner to approximate the double integral, where .

Use polar coordinates to find the volume of the solid under the paraboloid and above the disk .

Evaluate the iterated integral

Identify the surface with equation

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.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

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Exam 15: Multiple Integrals

Use polar coordinates to find the volume of the solid bounded by the paraboloid and the plane .

For which of the following regions would you use rectangular coordinates?

Evaluate the iterated integral.

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.

Use the Midpoint Rule with four squares of equal size to estimate the double integral.

Find the mass and the moments of inertia and and the radii of gyration and for the lamina occupying the region R, where R is the region bounded by the graphs of the equations and and having the mass density

Calculate the iterated integral.

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

Sketch the solid whose volume is given by the integral Evaluate the integral.

Use cylindrical coordinates to evaluate where E is the region that lies inside the cylinder and between the planes . Round the answer to two decimal places.

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

Evaluate where and T is the region bounded by the paraboloid and the plane

Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid .

Use polar coordinates to evaluate.

Find the mass and the moments of inertia and and the radii of gyration and for the lamina occupying the region R, where R is the rectangular region with vertices and , and having uniform density

Find an approximation for the integral. Use a double Riemann sum with and the sample point in the upper right corner to approximate the double integral, where .

Use polar coordinates to find the volume of the solid under the paraboloid and above the disk .

Evaluate the iterated integral

Identify the surface with equation

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.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

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

Final Exam

Filters