Question 1

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

Question 2

Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius   and density 1 about a diameter of its base.

Accepted Answer

A) 195.22 
B)    
C) 205.13 
D) 198.08 
E) 213.5 
A) 195.22 
B)    
C) 205.13 
D) 198.08 
E) 213.5

Question 3

Use polar coordinates to find the volume of the sphere of radius   . Round to two decimal places.

Accepted Answer

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

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 region in the first quadrant bounded by the lines   and the hyperbolas   .

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Evaluate the double integral.   ,   is triangular region with vertices   .

Accepted Answer

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

Question 8

Use spherical coordinates to find the volume of the solid that lies within the sphere   above the xy-plane and below the cone   . Round the answer to two decimal places.

Accepted Answer

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

Question 9

Use cylindrical coordinates to evaluate   where T is the solid bounded by the cylinder   and the planes   and

Accepted Answer

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

Question 10

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 11

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

Accepted Answer

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

Question 12

Use a triple integral to find the volume of the solid bounded by   and the planes   and   .

Accepted Answer

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

Question 13

Use polar coordinates to evaluate.

Accepted Answer

The answer of Use polar coordinates to evaluate.  ...

Question 14

Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral   , where f 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 15

Find the mass of the solid S bounded by the paraboloid   and the plane   if S has constant density 3.

Accepted Answer

A) 15.07 
B) 16.25 
C) 24.91 
D) 13.92 
E) 19.63 
A) 15.07 
B) 16.25 
C) 24.91 
D) 13.92 
E) 19.63

Question 16

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 17

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,...

Question 18

Identify the surface with equation

Accepted Answer

Upper half of a righ

Question 19

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 20

Identify the surface with equation

Accepted Answer

Plane parallel to th

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

Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius and density 1 about a diameter of its base.

Use polar coordinates to find the volume of the sphere of radius . Round to two decimal places.

Evaluate the integral by reversing the order of integration.

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

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

Evaluate the double integral. , is triangular region with vertices .

Use spherical coordinates to find the volume of the solid that lies within the sphere above the xy-plane and below the cone . Round the answer to two decimal places.

Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and

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

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

Use a triple integral to find the volume of the solid bounded by and the planes and .

Use polar coordinates to evaluate.

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

Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.

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 .

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

Identify the surface with equation

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

Identify the surface with equation

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Vector Calculus

Filters

Exam 12: Multiple Integrals

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

Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius and density 1 about a diameter of its base.

Use polar coordinates to find the volume of the sphere of radius . Round to two decimal places.

Evaluate the integral by reversing the order of integration.

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

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

Evaluate the double integral. , is triangular region with vertices .

Use spherical coordinates to find the volume of the solid that lies within the sphere above the xy-plane and below the cone . Round the answer to two decimal places.

Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and

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

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

Use a triple integral to find the volume of the solid bounded by and the planes and .

Use polar coordinates to evaluate.

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

Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.

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 .

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

Identify the surface with equation

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

Identify the surface with equation

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Vector Calculus

Filters