Question 1

Use a triple integral to find the volume of the tetrahedron enclosed by 10x + 10y + z = 2 and the coordinate planes.

Accepted Answer

The answer of Use a triple integral to find the...

Question 2

Find the surface area of the portion of the cone   that is above the region in the first quadrant bounded by the line   , and the parabola   .

Accepted Answer

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

Question 3

Find the volume of the solid in the first octant enclosed by x2 + y2 = 25, y = z, and z = 0.

Accepted Answer

Question 4

Find the Jacobian if x = 5u + w, y = vw, and z = u2v - 9.

Accepted Answer

A)  5u2v - 2uw 
B)  5u2v + 2uw2 
C)  10(u2v + uw2) 
D)  -10(u2v + uw2) 
E)  5u2v - 2uvw 
A)  5u2v - 2uw 
B)  5u2v + 2uw2 
C)  10(u2v + uw2) 
D)  -10(u2v + uw2) 
E)  5u2v - 2uvw

Question 5

Find the Jacobian   if   ,   and   .

Accepted Answer

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

Question 6

Find the volume of the solid bounded by   and the rectangle R = [0, 2] * [0, 2].

Accepted Answer

A)  32 cubic units 
B)  16 cubic units 
C)  8 cubic units 
D)  24 cubic units 
E)  128 cubic units 
A)  32 cubic units 
B)  16 cubic units 
C)  8 cubic units 
D)  24 cubic units 
E)  128 cubic units

Question 7

Find the volume of the solid that is enclosed by z = 5(x2 + y2), y = 2x, y = x2, and z = 0.

Accepted Answer

Question 8

Use a triple integral to find the volume of the solid in the first octant enclosed by
z = x2 + y2, y = x, and x = 1.

Accepted Answer

Question 9

The cylindrical parameterization of   is

Accepted Answer

A)  x = r cos $\theta$, y = r sin $\theta$, z = e r 
B)  x = r sin $\theta$, y = r cos $\theta$, z = e r 
C)  x = r cos $\theta$, y = r sin $\theta$, z = 3e r sin  $\theta$ 
D)  x = r sin $\theta$, y = r cos $\theta$, z = 3e r sin  $\theta$ 
E)  x = r cos $\theta$, y = r sin$\theta$, z = 3r2e r sin  $\theta$ 
A)  x = r cos $\theta$, y = r sin $\theta$, z = e r 
B)  x = r sin $\theta$, y = r cos $\theta$, z = e r 
C)  x = r cos $\theta$, y = r sin $\theta$, z = 3e r sin  $\theta$ 
D)  x = r sin $\theta$, y = r cos $\theta$, z = 3e r sin  $\theta$ 
E)  x = r cos $\theta$, y = r sin$\theta$, z = 3r2e r sin  $\theta$

Question 10

The centroid of a rectangular solid in the first octant with vertices (0, 0, 0), (0, 11, 0), and (11, 0, 11) is

Accepted Answer

A)    
B)  (1, 1, 1) 
C)    
D)    
E)    
A)    
B)  (1, 1, 1) 
C)    
D)    
E)

Question 11

Find   where R is the region in the first quadrant enclosed between   ,   , and x = 1.

Accepted Answer

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

Question 12

Evaluate   .

Accepted Answer

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

Question 13

Use a double integral in polar coordinates to find the volume enclosed by z = 0,
x + 2y - z = -4, and the cylinder x2 + y2 = 1.

Accepted Answer

The answer of Use a double integral in polar coordinates...

Question 14

Find the volume of the solid in the first octant enclosed by   , z = 0, y = 8, x = 0, and x - y + 2z = 2.

Accepted Answer

13.066667

Question 15

Use an appropriate transform to find the area of the region in the first quadrant enclosed by x + y = 1, x + y = 2, 3x - 2y = 2, and 3x - 2y = 5.

Accepted Answer

The answer of Use an appropriate transform to find the...

Question 16

A lamina with density  $\delta$(x, y) = 2x2 + y2 is bounded by x = y, x = 0, y = 0, y = 2. Find its moment of inertia about the x-axis.

Accepted Answer

A)    
B)  8 
C)    
D)    
E)    
A)    
B)  8 
C)    
D)    
E)

Question 17

The cylindrical parameterization of   is

Accepted Answer

A)  x = r cos$\theta$, y = r sin$\theta$,   
B)  x = r sin $\theta$, y = r cos$\theta$,   
C)  x = r cos $\theta$, y = r sin $\theta$,   
D)  x = r sin $\theta$, y = r cos $\theta$, z = 2 
E)  x = r cos$\theta$, y = r sin$\theta$,   
A)  x = r cos$\theta$, y = r sin$\theta$,   
B)  x = r sin $\theta$, y = r cos$\theta$,   
C)  x = r cos $\theta$, y = r sin $\theta$,   
D)  x = r sin $\theta$, y = r cos $\theta$, z = 2 
E)  x = r cos$\theta$, y = r sin$\theta$,

Question 18

Find the Jacobian,   ; u = 8 + 3x + y, v = 2x - y.

Accepted Answer

The answer of Find the Jacobian,   ; u...

Question 19

Find the centroid of the lamina enclosed by y = x2 and the line y = 4.

Accepted Answer

Question 20

Find   , if

Accepted Answer

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

Use a triple integral to find the volume of the tetrahedron enclosed by 10x + 10y + z = 2 and the coordinate planes.

Find the surface area of the portion of the cone that is above the region in the first quadrant bounded by the line , and the parabola .

Find the volume of the solid in the first octant enclosed by x² + y² = 25, y = z, and z = 0.

Find the Jacobian if x = 5u + w, y = vw, and z = u²v - 9.

Find the Jacobian if , and .

Find the volume of the solid bounded by and the rectangle R = [0, 2] * [0, 2].

Find the volume of the solid that is enclosed by z = 5(x² + y²), y = 2x, y = x², and z = 0.

Use a triple integral to find the volume of the solid in the first octant enclosed by z = x² + y², y = x, and x = 1.

The cylindrical parameterization of is

The centroid of a rectangular solid in the first octant with vertices (0, 0, 0), (0, 11, 0), and (11, 0, 11) is

Find where R is the region in the first quadrant enclosed between , , and x = 1.

Evaluate .

Use a double integral in polar coordinates to find the volume enclosed by z = 0, x + 2y - z = -4, and the cylinder x² + y² = 1.

Find the volume of the solid in the first octant enclosed by , z = 0, y = 8, x = 0, and x - y + 2z = 2.

Use an appropriate transform to find the area of the region in the first quadrant enclosed by x + y = 1, x + y = 2, 3x - 2y = 2, and 3x - 2y = 5.

A lamina with density $\delta$ (x, y) = 2x² + y² is bounded by x = y, x = 0, y = 0, y = 2. Find its moment of inertia about the x-axis.

The cylindrical parameterization of is

Find the Jacobian, ; u = 8 + 3x + y, v = 2x - y.

Find the centroid of the lamina enclosed by y = x² and the line y = 4.

Find , if

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

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Infinte Series

Parametric and Polar Curves; Conic Sections

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Exam 14: Multiple Integrals

Use a triple integral to find the volume of the tetrahedron enclosed by 10x + 10y + z = 2 and the coordinate planes.

Find the surface area of the portion of the cone that is above the region in the first quadrant bounded by the line , and the parabola .

Find the volume of the solid in the first octant enclosed by x2 + y2 = 25, y = z, and z = 0.

Find the Jacobian if x = 5u + w, y = vw, and z = u2v - 9.

Find the Jacobian if , and .

Find the volume of the solid bounded by and the rectangle R = [0, 2] * [0, 2].

Find the volume of the solid that is enclosed by z = 5(x2 + y2), y = 2x, y = x2, and z = 0.

Use a triple integral to find the volume of the solid in the first octant enclosed by z = x2 + y2, y = x, and x = 1.

The cylindrical parameterization of is

The centroid of a rectangular solid in the first octant with vertices (0, 0, 0), (0, 11, 0), and (11, 0, 11) is

Find where R is the region in the first quadrant enclosed between , , and x = 1.

Evaluate .

Use a double integral in polar coordinates to find the volume enclosed by z = 0, x + 2y - z = -4, and the cylinder x2 + y2 = 1.

Find the volume of the solid in the first octant enclosed by , z = 0, y = 8, x = 0, and x - y + 2z = 2.

Use an appropriate transform to find the area of the region in the first quadrant enclosed by x + y = 1, x + y = 2, 3x - 2y = 2, and 3x - 2y = 5.

A lamina with density δ\deltaδ (x, y) = 2x2 + y2 is bounded by x = y, x = 0, y = 0, y = 2. Find its moment of inertia about the x-axis.

The cylindrical parameterization of is

Find the Jacobian, ; u = 8 + 3x + y, v = 2x - y.

Find the centroid of the lamina enclosed by y = x2 and the line y = 4.

Find , if

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Topics in Vector Calculus

Filters

Find the volume of the solid in the first octant enclosed by x² + y² = 25, y = z, and z = 0.

Find the Jacobian if x = 5u + w, y = vw, and z = u²v - 9.

Find the volume of the solid that is enclosed by z = 5(x² + y²), y = 2x, y = x², and z = 0.

Use a triple integral to find the volume of the solid in the first octant enclosed by z = x² + y², y = x, and x = 1.

Use a double integral in polar coordinates to find the volume enclosed by z = 0, x + 2y - z = -4, and the cylinder x² + y² = 1.

A lamina with density $\delta$ (x, y) = 2x² + y² is bounded by x = y, x = 0, y = 0, y = 2. Find its moment of inertia about the x-axis.

Find the centroid of the lamina enclosed by y = x² and the line y = 4.