Question 1

Identify the surface with equation

Accepted Answer

Plane parallel to the xy-plane and 10 units above it

Question 2

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

Accepted Answer

A)   
B)   
C)   
D)   
E)    B

Question 3

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)    C

Question 4

Evaluate the integral by reversing the order of integration.

Accepted Answer

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

Question 5

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

Accepted Answer

A)   208
B)   52
C)   312
D)   42
E)   343

Question 6

Express the volume of the wedge in the first octant that is cut from the cylinder  by the planes  and  as an iterated integral with respect to  ,then to  ,then to  .

Accepted Answer

The answer of Express the volume of the wedge in...

Question 7

Use spherical coordinates. Evaluate  ,where B is the ball with center the origin and radius 5.

Accepted Answer

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

Question 8

Evaluate the triple integral.Round your answer to one decimal place.   lies under the plane  and above the region in the  -plane bounded by the curves  ,and  .

Accepted Answer

The answer of Evaluate the triple integral.Round your answer to...

Question 9

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Find the mass of the lamina that occupies the region D and has the given density function.Round your answer to two decimal places.

Accepted Answer

The answer of Find the mass of the lamina that...

Question 11

Express the triple integral   as an iterated integral in six different ways using different orders of integration where T is the solid bounded by the planes    and

Accepted Answer

The answer of Express the triple integral   as...

Question 12

Evaluate the double integral.   is bounded by  and  .

Accepted Answer

The answer of Evaluate the double integral.   is...

Question 13

Evaluate the double integral  ,where  is the region bounded by the graphs of  and  .

Accepted Answer

The answer of Evaluate the double integral  ,where ...

Question 14

A swimming pool is circular with a 60-ft diameter.The depth is constant along east-west lines and increases linearly from 3 ft at the south end to 9 ft at the north end.Find the volume of water in the pool.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Evaluate the iterated integral  by reversing the order of integration.

Accepted Answer

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

Question 16

Use cylindrical coordinates to evaluate

Accepted Answer

A)    
B)    
C)    
D)

Question 17

Find the moment of inertia about the y-axis for a cube of constant density 3 and side length 6 if one vertex is located at the origin and three edges lie along the coordinate axes.

Accepted Answer

The answer of Find the moment of inertia about the...

Question 18

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

Accepted Answer

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

Question 19

An electric charge is spread over a rectangular region  Find the total charge on R if the charge density at a point  in R (measured in coulombs per square meter)is

Accepted Answer

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

Question 20

Find the mass of the solid E,if E is the cube given by  and the density function  is  .

Accepted Answer

The answer of Find the mass of the solid E,if...

Exam 12: Multiple Integrals

Identify the surface with equation

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

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.

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

Express the volume of the wedge in the first octant that is cut from the cylinder by the planes and as an iterated integral with respect to ,then to ,then to .

Use spherical coordinates. Evaluate ,where B is the ball with center the origin and radius 5.

Evaluate the triple integral.Round your answer to one decimal place. lies under the plane and above the region in the -plane bounded by the curves ,and .

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

Find the mass of the lamina that occupies the region D and has the given density function.Round your answer to two decimal places.

Express the triple integral as an iterated integral in six different ways using different orders of integration where T is the solid bounded by the planes and

Evaluate the double integral. is bounded by and .

Evaluate the double integral ,where is the region bounded by the graphs of and .

A swimming pool is circular with a 60-ft diameter.The depth is constant along east-west lines and increases linearly from 3 ft at the south end to 9 ft at the north end.Find the volume of water in the pool.

Evaluate the iterated integral by reversing the order of integration.

Use cylindrical coordinates to evaluate

Find the moment of inertia about the y-axis for a cube of constant density 3 and side length 6 if one vertex is located at the origin and three edges lie along the coordinate axes.

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

An electric charge is spread over a rectangular region Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter) is

Find the mass of the solid E,if E is the cube given by and the density function is .