Question 1

Evaluate the iterated integral after changing coordinate systems.

Accepted Answer

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

Question 2

Find a transformation from a rectangular region S in the uv-plane to the region R which lies inside   outside   and in the first quadrant.

Accepted Answer

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

Question 3

Use a transformation to evaluate the double integral over the region R which is the region that lies inside   outside   and in the first quadrant.

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Question 4

Compute the volume of the solid bounded by the given surfaces.

Accepted Answer

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

Question 5

Find the mass and moments of inertia Ix and Iy for a lamina in the shape of the region bounded by   and   with density   .

Accepted Answer

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

Question 6

Evaluate the double integral.   R is bounded by y = 4x + 6, y = 4x + 7, y = -2x + 3, and y = -2x + 5

Accepted Answer

A)    
B)  -265 
C)    
D)  454 
A)    
B)  -265 
C)    
D)  454

Question 7

Write the equation   in cylindrical coordinates.

Accepted Answer

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

Question 8

Compute the volume of the solid bounded by the given surfaces.   and the three coordinate planes

Accepted Answer

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

Question 9

Suppose that   is the population density of a species of a certain small animal. Estimate the population in the triangular region     and   .

Accepted Answer

A)  2426 
B)  1115 
C)  2548 
D)  936 
A)  2426 
B)  1115 
C)  2548 
D)  936

Question 10

Find the center of mass of a lamina in the shape of   , with density

Accepted Answer

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

Question 11

Find the surface area of   between   ,   and   .

Accepted Answer

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

Question 12

Compute the volume of the solid Q bounded by   and   .

Accepted Answer

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

Question 13

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work.
R is bounded by y = x2, y = x2 + 3, y = 5 - x2, and y = 3 - x2

Accepted Answer

Answer details may vary.
The r

Question 14

Write the equation   in cylindrical coordinates.

Accepted Answer

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

Question 15

Numerically estimate the surface area of the portion of   inside of

Accepted Answer

A)  3.14 
B)  5.57 
C)  116.24 
D)  114.51 
A)  3.14 
B)  5.57 
C)  116.24 
D)  114.51

Question 16

Evaluate the double integral.

Accepted Answer

A)  208 
B)  304 
C)  -208 
D)  -304 
A)  208 
B)  304 
C)  -208 
D)  -304

Question 17

Calculate the mass of an object with density   and bounded by   and the planes   .

Accepted Answer

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

Question 18

Evaluate the double integral.

Accepted Answer

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

Question 19

Use an appropriate coordinate system to find the volume of a solid bounded by   .

Accepted Answer

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

Question 20

Use an appropriate coordinate system to find the volume of a solid lying outside the cones defined by   (includes the portion extending to z < 0) and inside the sphere defined by   .

Accepted Answer

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

Evaluate the iterated integral after changing coordinate systems.

Find a transformation from a rectangular region S in the uv-plane to the region R which lies inside outside and in the first quadrant.

Use a transformation to evaluate the double integral over the region R which is the region that lies inside outside and in the first quadrant.

Compute the volume of the solid bounded by the given surfaces.

Find the mass and moments of inertia I_x and I_y for a lamina in the shape of the region bounded by and with density .

Evaluate the double integral. R is bounded by y = 4x + 6, y = 4x + 7, y = -2x + 3, and y = -2x + 5

Write the equation in cylindrical coordinates.

Compute the volume of the solid bounded by the given surfaces. and the three coordinate planes

Suppose that is the population density of a species of a certain small animal. Estimate the population in the triangular region and .

Find the center of mass of a lamina in the shape of , with density

Find the surface area of between , and .

Compute the volume of the solid Q bounded by and .

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work. R is bounded by y = x², y = x² + 3, y = 5 - x², and y = 3 - x²

Write the equation in cylindrical coordinates.

Numerically estimate the surface area of the portion of inside of

Evaluate the double integral.

Calculate the mass of an object with density and bounded by and the planes .

Evaluate the double integral.

Use an appropriate coordinate system to find the volume of a solid bounded by .

Use an appropriate coordinate system to find the volume of a solid lying outside the cones defined by (includes the portion extending to z < 0) and inside the sphere defined by .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Vector Calculus

Second Order Differential Equations

Filters

Exam 14: Multiple Integrals

Evaluate the iterated integral after changing coordinate systems.

Find a transformation from a rectangular region S in the uv-plane to the region R which lies inside outside and in the first quadrant.

Use a transformation to evaluate the double integral over the region R which is the region that lies inside outside and in the first quadrant.

Compute the volume of the solid bounded by the given surfaces.

Find the mass and moments of inertia Ix and Iy for a lamina in the shape of the region bounded by and with density .

Evaluate the double integral. R is bounded by y = 4x + 6, y = 4x + 7, y = -2x + 3, and y = -2x + 5

Write the equation in cylindrical coordinates.

Compute the volume of the solid bounded by the given surfaces. and the three coordinate planes

Suppose that is the population density of a species of a certain small animal. Estimate the population in the triangular region and .

Find the center of mass of a lamina in the shape of , with density

Find the surface area of between , and .

Compute the volume of the solid Q bounded by and .

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work. R is bounded by y = x2, y = x2 + 3, y = 5 - x2, and y = 3 - x2

Write the equation in cylindrical coordinates.

Numerically estimate the surface area of the portion of inside of

Evaluate the double integral.

Calculate the mass of an object with density and bounded by and the planes .

Evaluate the double integral.

Use an appropriate coordinate system to find the volume of a solid bounded by .

Use an appropriate coordinate system to find the volume of a solid lying outside the cones defined by (includes the portion extending to z < 0) and inside the sphere defined by .

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Vector Calculus

Second Order Differential Equations

Filters

Find the mass and moments of inertia I_x and I_y for a lamina in the shape of the region bounded by and with density .

Find a transformation from a rectangular region S in the uv-plane to the region R. Show all your work. R is bounded by y = x², y = x² + 3, y = 5 - x², and y = 3 - x²