Question 1

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...

Question 2

Express the integral as an iterated integral of the form   where E is the solid bounded by the surfaces

Accepted Answer

The answer of Express the integral as an iterated integral...

Question 3

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 4

Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length   if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at   , and that the sides are along the positive axes.

Accepted Answer

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

Question 5

Calculate the iterated integral.

Accepted Answer

The answer of Calculate the iterated integral.  ...

Question 6

Use cylindrical coordinates to evaluate

Accepted Answer

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

Question 7

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)    
A)    
B)    
C)    
D)    
E)

Question 8

Evaluate the iterated integral   by reversing the order of integration.

Accepted Answer

The answer of Evaluate the iterated integral   by...

Question 9

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

Accepted Answer

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

Question 10

Evaluate   where   is the figure bounded by   and   .

Accepted Answer

The answer of Evaluate   where   is...

Question 11

An agricultural sprinkler distributes water in a circular pattern of radius   ft. It supplies water to a depth of   feet per hour at a distance of   feet from the sprinkler. What is the total amount of water supplied per hour to the region inside the circle of radius   feet centered at the sprinkler?

Accepted Answer

The answer of An agricultural sprinkler distributes water in a...

Question 12

Find the Jacobian of the transformation.

Accepted Answer

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

Question 13

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

Question 14

Find the moment of inertia about the y-axis for a cube of constant density 3 and side length   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 15

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

Accepted Answer

The answer of Calculate the double integral. Round your answer...

Question 16

Evaluate the integral by reversing the order of integration.

Accepted Answer

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

Question 17

Find the mass of the lamina that occupies the region   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 18

Use a double integral to find the area of the region R where R is bounded by the circle

Accepted Answer

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

Question 19

Use polar coordinates to find the volume of the solid under the paraboloid   and above the disk   .

Accepted Answer

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

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

Express the integral as an iterated integral of the form where E is the solid bounded by the surfaces

Calculate the iterated integral.

Calculate the iterated integral.

Use cylindrical coordinates to evaluate

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 iterated integral by reversing the order of integration.

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

Evaluate where is the figure bounded by and .

An agricultural sprinkler distributes water in a circular pattern of radius ft. It supplies water to a depth of feet per hour at a distance of feet from the sprinkler. What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler?

Find the Jacobian of the transformation.

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

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

Evaluate the integral by reversing the order of integration.

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

Use a double integral to find the area of the region R where R is bounded by the circle

Use polar coordinates to find the volume of the solid under the paraboloid and above the disk .

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

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Exam 12: Multiple Integrals

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

Express the integral as an iterated integral of the form where E is the solid bounded by the surfaces

Calculate the iterated integral.

Calculate the iterated integral.

Use cylindrical coordinates to evaluate

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 iterated integral by reversing the order of integration.

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

Evaluate where is the figure bounded by and .

An agricultural sprinkler distributes water in a circular pattern of radius ft. It supplies water to a depth of feet per hour at a distance of feet from the sprinkler. What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler?

Find the Jacobian of the transformation.

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

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

Evaluate the integral by reversing the order of integration.

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

Use a double integral to find the area of the region R where R is bounded by the circle

Use polar coordinates to find the volume of the solid under the paraboloid and above the disk .

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