Question 1

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 the equations   and  and having the mass density

Accepted Answer

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

Question 2

Find the area of the part of the sphere  that lies inside the paraboloid  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Find the volume of the solid bounded by the surface  and the planes  and coordinate planes.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 4

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

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  , and having the mass density

Accepted Answer

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

Question 6

Use the given transformation to evaluate the integral.  , where R is the region in the first quadrant bounded by the lines  and the hyperbolas  .

Accepted Answer

A) 8.841 
B) 3.296 
C) 4.447 
D) 5.088 
E) 9.447

Question 7

Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places.  R is the parallelogram bounded by the lines  .

Accepted Answer

The answer of Evaluate the integral by making an appropriate...

Question 8

Evaluate the double integral.   is bounded by the circle with center the origin and radius  .

Accepted Answer

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

Question 9

Calculate the iterated integral. Round your answer to two decimal places.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Identify the surface with equation

Accepted Answer

The answer of Identify the surface with equation ...

Question 11

Find the volume of the solid bounded in the first octanat bounded by the cylinder  and the planes  .

Accepted Answer

The answer of Find the volume of the solid bounded...

Question 12

Use cylindrical coordinates to evaluate

Accepted Answer

A)    
B)    
C)    
D)

Question 13

Find  , if  .

Accepted Answer

The answer of Find  , if  ....

Question 14

Find the exact area of the surface.  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

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

Accepted Answer

A) 3.4 
B) 0 
C) 8.57 
D) 0.54 
E) 9.19

Question 16

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

Accepted Answer

A)    
B)   
C)   
D)    
E)

Question 17

Calculate the iterated integral.

Accepted Answer

A)   
B) 8 
C)   
D)   
E) None of these

Question 18

Find the area of the part of the plane  that lies in the first octant.

Accepted Answer

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

Question 19

Use spherical coordinate to find the volume above the cone  and inside sphere  .

Accepted Answer

The answer of Use spherical coordinate to find the volume...

Question 20

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

Accepted Answer

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

Exam 15: Multiple Integrals

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 the equations and and having the mass density

Find the area of the part of the sphere that lies inside the paraboloid .

Find the volume of the solid bounded by the surface and the planes and coordinate planes.

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

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

Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas .

Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places. R is the parallelogram bounded by the lines .

Evaluate the double integral. is bounded by the circle with center the origin and radius .

Calculate the iterated integral. Round your answer to two decimal places.

Identify the surface with equation

Find the volume of the solid bounded in the first octanat bounded by the cylinder and the planes .

Use cylindrical coordinates to evaluate

Find , if .

Find the exact area of the surface. .

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

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

Calculate the iterated integral.

Find the area of the part of the plane that lies in the first octant.

Use spherical coordinate to find the volume above the cone and inside sphere .

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