Question 1

Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places.

Accepted Answer

A)  29.20 
B)  58.39 
C)  439.36 
D)  36.18 
E)  1.64 
A)  29.20 
B)  58.39 
C)  439.36 
D)  36.18 
E)  1.64

Question 2

Consider the region   in the xy-plane bounded by the ellipse   and the transformation   and   . Find   .

Accepted Answer

A)    
B)  0 
C)    
D)    
E)    
A)    
B)  0 
C)    
D)    
E)

Question 3

Evaluate the following improper integral.

Accepted Answer

A)    
B)    
C)    
D)    
E)  The integral does not converge. 
A)    
B)    
C)    
D)    
E)  The integral does not converge.

Question 4

Evaluate the improper iterated integral   .

Accepted Answer

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

Question 5

Evaluate the iterated integral   .

Accepted Answer

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

Question 6

Evaluate the integral   by switching the order of integration. Round your answer to two decimal places.

Accepted Answer

A)  5.16 
B)  48.66 
C)  15.38 
D)  13.38 
E)  56.14 
A)  5.16 
B)  48.66 
C)  15.38 
D)  13.38 
E)  56.14

Question 7

Evaluate the iterated integral   by converting to polar coordinates. Round your answer to four decimal places.

Accepted Answer

A)  9.2525 
B)  13.2525 
C)  14.2525 
D)  19.2525 
E)  10.2525 
A)  9.2525 
B)  13.2525 
C)  14.2525 
D)  19.2525 
E)  10.2525

Question 8

Evaluate the iterated integral   by converting to polar coordinates.

Accepted Answer

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

Question 9

Evaluate the following iterated integral.

Accepted Answer

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

Question 10

Use a double integral to find the area enclosed by the graph of   .

Accepted Answer

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

Question 11

Find the Jacobian for the indicated change of variables.   ,

Accepted Answer

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

Question 12

Evaluate the following iterated integral.

Accepted Answer

A)  43 
B)  42 
C)  36 
D)  33 
E)  38 
A)  43 
B)  42 
C)  36 
D)  33 
E)  38

Question 13

The area of a region R is given by the iterated integral   . Switch the order of integration and show that both orders yield the same area. What is this area?

Accepted Answer

A)  101 
B)  20 
C)  30 
D)  10 
E)  5 
A)  101 
B)  20 
C)  30 
D)  10 
E)  5

Question 14

Identify the region of integration for the following integral.

Accepted Answer

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

Question 15

Evaluate the following iterated integral.

Accepted Answer

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

Question 16

A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object.

Accepted Answer

A)    cm3  
B)    cm3  
C)    cm3  
D)    cm3  
E)    cm3  
A)    cm3  
B)    cm3  
C)    cm3  
D)    cm3  
E)    cm3

Question 17

Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below.

Accepted Answer

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

Question 18

Rewrite the iterated integral   using the order dydxdz. ​
​

Accepted Answer

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

Question 19

Find   of the center of mass of the solid of given density   bounded by the graphs of the equations   . ​

Accepted Answer

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

Question 20

Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations   if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.

Accepted Answer

A)  1.2983 
B)  36.5966 
C)  3.2983 
D)  5.5966 
E)  37.2983 
A)  1.2983 
B)  36.5966 
C)  3.2983 
D)  5.5966 
E)  37.2983

Find the area of the portion of the surface that lies above the region . Round your answer to two decimal places.

Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find .

Evaluate the following improper integral.

Evaluate the improper iterated integral .

Evaluate the iterated integral .

Evaluate the integral by switching the order of integration. Round your answer to two decimal places.

Evaluate the iterated integral by converting to polar coordinates. Round your answer to four decimal places.

Evaluate the iterated integral by converting to polar coordinates.

Evaluate the following iterated integral.

Use a double integral to find the area enclosed by the graph of .

Find the Jacobian for the indicated change of variables. ,

Evaluate the following iterated integral.

The area of a region R is given by the iterated integral . Switch the order of integration and show that both orders yield the same area. What is this area?

Identify the region of integration for the following integral.

Evaluate the following iterated integral.

A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object.

Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below.

Rewrite the iterated integral using the order dydxdz.

Find of the center of mass of the solid of given density bounded by the graphs of the equations .

Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Vector Anal

Filters

Exam 14: Multiple Integration

Find the area of the portion of the surface that lies above the region . Round your answer to two decimal places.

Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find .

Evaluate the following improper integral.

Evaluate the improper iterated integral .

Evaluate the iterated integral .

Evaluate the integral by switching the order of integration. Round your answer to two decimal places.

Evaluate the iterated integral by converting to polar coordinates. Round your answer to four decimal places.

Evaluate the iterated integral by converting to polar coordinates.

Evaluate the following iterated integral.

Use a double integral to find the area enclosed by the graph of .

Find the Jacobian for the indicated change of variables. ,

Evaluate the following iterated integral.

The area of a region R is given by the iterated integral . Switch the order of integration and show that both orders yield the same area. What is this area?

Identify the region of integration for the following integral.

Evaluate the following iterated integral.

A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object.

Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below.

Rewrite the iterated integral using the order dydxdz. ​ ​

Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​

Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Vector Anal

Filters

Rewrite the iterated integral using the order dydxdz.

Find of the center of mass of the solid of given density bounded by the graphs of the equations .