Question 1

Let V be the volume of the solid generated by revolving the region enclosed by about $x = - y ^ { 2 },$ Then V is

Accepted Answer

A)  $\frac { 5 \pi } { 3 }$ 
B)  $\frac { \pi } { 5 }$ 
C)  $24 \pi$ 
D)  $\frac { 1088 \pi } { 15 }$ 
E)  $\frac { 8 \pi } { 5 }$ 
A)  $\frac { 5 \pi } { 3 }$ 
B)  $\frac { \pi } { 5 }$ 
C)  $24 \pi$ 
D)  $\frac { 1088 \pi } { 15 }$ 
E)  $\frac { 8 \pi } { 5 }$

Question 2

The work done by a variable force $F ( x ) = ( 2 x + 1 ) ^ { 2 }$ Newtons that moves an object along a straight line in the direction of F from x = 2 meters to x = 4 meters, in Newton-meters, is

Accepted Answer

A)  $\frac { 50 } { 3 }$ 
B)  $\frac { 68 } { 3 }$ 
C)  $\frac { 255 } { 3 }$ 
D)  $\frac { 289 } { 3 }$ 
E)  $\frac { 302 } { 3 }$ 
A)  $\frac { 50 } { 3 }$ 
B)  $\frac { 68 } { 3 }$ 
C)  $\frac { 255 } { 3 }$ 
D)  $\frac { 289 } { 3 }$ 
E)  $\frac { 302 } { 3 }$

Question 3

A trough whose cross-section is a trapezoid whose lower base is 4 feet long and upper base is 6 feet long, and is 4 feet high is filled with of water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

Accepted Answer

A)  $3,000$ 
B)  $\frac { 8,000 } { 3 }$ 
C)  $\frac { 7,000 } { 3 }$ 
D)  $2,000$ 
E)  $2,250$ 
A)  $3,000$ 
B)  $\frac { 8,000 } { 3 }$ 
C)  $\frac { 7,000 } { 3 }$ 
D)  $2,000$ 
E)  $2,250$

Let V be the volume of the solid generated by revolving the region enclosed by about $x = - y ^ { 2 },$ Then V is

The work done by a variable force $F ( x ) = ( 2 x + 1 ) ^ { 2 }$ Newtons that moves an object along a straight line in the direction of F from x = 2 meters to x = 4 meters, in Newton-meters, is

A trough whose cross-section is a trapezoid whose lower base is 4 feet long and upper base is 6 feet long, and is 4 feet high is filled with of water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

Applications of the Derivative

The Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Exam 7: Applications of the Integral

Let V be the volume of the solid generated by revolving the region enclosed by about x=−y2,x = - y ^ { 2 },x=−y2, Then V is

The work done by a variable force F(x)=(2x+1)2F ( x ) = ( 2 x + 1 ) ^ { 2 }F(x)=(2x+1)2 Newtons that moves an object along a straight line in the direction of F from x = 2 meters to x = 4 meters, in Newton-meters, is

A trough whose cross-section is a trapezoid whose lower base is 4 feet long and upper base is 6 feet long, and is 4 feet high is filled with of water of density 62.5 pounds per cubic foot. The force, in pounds, due to hydrostatic pressure on one end of the trough is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

Applications of the Derivative

The Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Let V be the volume of the solid generated by revolving the region enclosed by about $x = - y ^ { 2 },$ Then V is

The work done by a variable force $F ( x ) = ( 2 x + 1 ) ^ { 2 }$ Newtons that moves an object along a straight line in the direction of F from x = 2 meters to x = 4 meters, in Newton-meters, is