Question 1

Integrate the function   over the region bounded by     and

Accepted Answer

The answer of Integrate the function   over the...

Question 2

Let D be the region   , and let   . 
A) Find the region   in the   - plane to which   is transformed by the mapping   . 
B) Compute the integral using the variables   . (Use the convenient order of integration.)

Accepted Answer

A) @#IMG-DLM& is the triangle

Question 3

Consider the integral   
A) Draw the region of integration and reverse the order of integration.
B) Compute the integral in any order you choose.

Accepted Answer

The answer of Consider the integral   
A) Draw...

Question 4

Let   ,   , and   Which of the following statements holds?

Accepted Answer

A)    . 
B)    but   . 
C)    but   . 
D)    but   . 
E)  The three integrals are different. 
A)    . 
B)    but   . 
C)    but   . 
D)    but   . 
E)  The three integrals are different.

Question 5

Let   , where   is the region defined by the inequalities   .
Use the change of variables formula to determine which of the following is true.

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these answers is true. 
A)    
B)    
C)    
D)    
E)  None of these answers is true.

Question 6

Let   and   be the triangle in the   plane enclosed by the lines   .
Find the set of all the points   in   such that

Accepted Answer

@#IMG-DLM& @#IMG-DLM& is the part of the

Question 7

Let   be the parallelogram bounded by the lines   
A) Find a linear mapping   that maps   to   
B) Use the linear mapping   to evaluate

Accepted Answer

The answer of Let   be the parallelogram bounded...

Question 8

Let   be the parallelogram with vertices   
A) Find a linear mapping   that maps   to   
B) Use the linear mapping   to evaluate

Accepted Answer

The answer of Let   be the parallelogram with...

Question 9

Let   be the region in the   space defined by the inequalities   
A) Rewrite the inequalities for   in adequate form for evaluating   in the order   . 
B) Evaluate the integral   .

Accepted Answer

The answer of Let   be the region in...

Question 10

Find the area bounded by the curves   and   .

Accepted Answer

The answer of Find the area bounded by the curves...

Question 11

Use spherical coordinates to set up the integral to compute the volume of the solid bounded by the paraboloid   and the upper sphere   . (Do not evaluate the integral.)

Accepted Answer

The answer of Use spherical coordinates to set up the...

Question 12

Integrate the function   over the region bounded by the cone   and the paraboloid

Accepted Answer

The answer of Integrate the function   over the...

Question 13

Convert the following integral to cylindrical and spherical coordinates:   .

Accepted Answer

Cylindrica

Question 14

Evaluate the   , where   is the region   .
Sketch the region of integration.

Accepted Answer

The answer of Evaluate the   , where ...

Question 15

The Jacobian of   at the point   is which of the following?

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of these answers is correct. 
A)    
B)    
C)    
D)    
E)  None of these answers is correct.

Question 16

Find the center of mass of the tetrahedron   in the first octant formed by the coordinate planes and the plane   . (Assume the density is   .)

Accepted Answer

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

Question 17

Find the volume of the ellipsoid

Accepted Answer

The answer of Find the volume of the ellipsoid ...

Question 18

The value of the integral   is which of the following?

Accepted Answer

A)    
B)    
C)    
D)  1 
E)  None of the above. 
A)    
B)    
C)    
D)  1 
E)  None of the above.

Integrate the function over the region bounded by and

Let D be the region , and let . A) Find the region in the - plane to which is transformed by the mapping . B) Compute the integral using the variables . (Use the convenient order of integration.)

Consider the integral A) Draw the region of integration and reverse the order of integration. B) Compute the integral in any order you choose.

Let , , and Which of the following statements holds?

Let , where is the region defined by the inequalities . Use the change of variables formula to determine which of the following is true.

Let and be the triangle in the plane enclosed by the lines . Find the set of all the points in such that

Let be the parallelogram bounded by the lines A) Find a linear mapping that maps to B) Use the linear mapping to evaluate

Let be the parallelogram with vertices A) Find a linear mapping that maps to B) Use the linear mapping to evaluate

Let be the region in the space defined by the inequalities A) Rewrite the inequalities for in adequate form for evaluating in the order . B) Evaluate the integral .

Find the area bounded by the curves and .

Use spherical coordinates to set up the integral to compute the volume of the solid bounded by the paraboloid and the upper sphere . (Do not evaluate the integral.)

Integrate the function over the region bounded by the cone and the paraboloid

Convert the following integral to cylindrical and spherical coordinates: .

Evaluate the , where is the region . Sketch the region of integration.

The Jacobian of at the point is which of the following?

Find the center of mass of the tetrahedron in the first octant formed by the coordinate planes and the plane . (Assume the density is .)

Find the volume of the ellipsoid

The value of the integral is which of the following?

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters

Exam 16: Multiple Integration

Integrate the function over the region bounded by and

Let D be the region , and let . A) Find the region in the - plane to which is transformed by the mapping . B) Compute the integral using the variables . (Use the convenient order of integration.)

Consider the integral A) Draw the region of integration and reverse the order of integration. B) Compute the integral in any order you choose.

Let , , and Which of the following statements holds?

Let , where is the region defined by the inequalities . Use the change of variables formula to determine which of the following is true.

Let and be the triangle in the plane enclosed by the lines . Find the set of all the points in such that

Let be the parallelogram bounded by the lines A) Find a linear mapping that maps to B) Use the linear mapping to evaluate

Let be the parallelogram with vertices A) Find a linear mapping that maps to B) Use the linear mapping to evaluate

Let be the region in the space defined by the inequalities A) Rewrite the inequalities for in adequate form for evaluating in the order . B) Evaluate the integral .

Find the area bounded by the curves and .

Use spherical coordinates to set up the integral to compute the volume of the solid bounded by the paraboloid and the upper sphere . (Do not evaluate the integral.)

Integrate the function over the region bounded by the cone and the paraboloid

Convert the following integral to cylindrical and spherical coordinates: .

Evaluate the , where is the region . Sketch the region of integration.

The Jacobian of at the point is which of the following?

Find the center of mass of the tetrahedron in the first octant formed by the coordinate planes and the plane . (Assume the density is .)

Find the volume of the ellipsoid

The value of the integral is which of the following?

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters