Question 1

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

Accepted Answer

A)   
B)   
C)   
D)   
E)    A

Question 2

Calculate the iterated integral.

Accepted Answer

The answer of Calculate the iterated integral. ...

Question 3

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

Accepted Answer

The answer of Evaluate  where  and T is...

Question 4

Calculate the iterated integral.Round yourAnswer to two decimal places.

Accepted Answer

The answer of Calculate the iterated integral.Round yourAnswer to two...

Question 5

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

Accepted Answer

The answer of Use cylindrical or spherical coordinates, whichever seems...

Question 6

Calculate the iterated integral.

Accepted Answer

The answer of Calculate the iterated integral. ...

Question 7

Find the Jacobian of the transformation.

Accepted Answer

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

Question 8

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

Accepted Answer

The answer of Use cylindrical coordinates to evaluate the triple...

Question 9

Find the area of the surface S where S is the part of the sphere  that lies to the right of the xz-plane and inside the cylinder

Accepted Answer

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

Question 10

Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral  where  is a continuous function.Then write an expression for the (iterated) integral.

Accepted Answer

The answer of Determine whether to use polar coordinates or...

Question 11

An agricultural sprinkler distributes water in a circular pattern of radius  ft.It supplies water to a depth of  feet per hour at a distance of  feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius  feet centered at the sprinkler?

Accepted Answer

The answer of An agricultural sprinkler distributes water in a...

Question 12

Evaluate the iterated integral by converting to polar coordinates.Round theAnswer to two decimal places.

Accepted Answer

The answer of Evaluate the iterated integral by converting to...

Question 13

Evaluate the triple integral.Round yourAnswer to one decimal place.

Accepted Answer

The answer of Evaluate the triple integral.Round yourAnswer to one...

Question 14

Evaluate the iterated integral.

Accepted Answer

The answer of Evaluate the iterated integral. ...

Question 15

Select the correct Answer for each question.
-Use spherical coordinates.Evaluate  here  is the ball with center the origin and radius

Accepted Answer

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

Question 16

The sketch of the solid is given below.Given  write the inequalities that describe it.Select the correct Answer

Accepted Answer

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

Question 17

Select the correct Answer for each question.
-Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola  and the x-axis.

Accepted Answer

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

Question 18

The sketch of the solid is given below.Given  , write the inequalities that describe it.

Accepted Answer

The answer of The sketch of the solid is given...

Question 19

Select the correct Answer for each question.
-Calculate the double integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Find the volume under  and above the region bounded by  and  .

Accepted Answer

The answer of Find the volume under  and above...

Exam 15: Multiple Integrals

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

Calculate the iterated integral.

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

Calculate the iterated integral.Round yourAnswer to two decimal places.

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

Calculate the iterated integral.

Find the Jacobian of the transformation.

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

Find the area of the surface S where S is the part of the sphere that lies to the right of the xz-plane and inside the cylinder

Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral where is a continuous function.Then write an expression for the (iterated) integral.

An agricultural sprinkler distributes water in a circular pattern of radius ft.It supplies water to a depth of feet per hour at a distance of feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler?

Evaluate the iterated integral by converting to polar coordinates.Round theAnswer to two decimal places.

Evaluate the triple integral.Round yourAnswer to one decimal place.

Evaluate the iterated integral.

Select the correct Answer for each question. -Use spherical coordinates.Evaluate here is the ball with center the origin and radius

The sketch of the solid is given below.Given write the inequalities that describe it.Select the correct Answer

Select the correct Answer for each question. -Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis.

The sketch of the solid is given below.Given , write the inequalities that describe it.

Select the correct Answer for each question. -Calculate the double integral.

Find the volume under and above the region bounded by and .