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)    
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)    
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)    
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)    ,   
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 
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.   ...

Question 9

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

Accepted Answer

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

Question 10

Identify the surface with equation

Accepted Answer

Sphere wit

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

Question 17

Calculate the iterated integral.

Accepted Answer

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

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.

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

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.

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