Question 1

Evaluate the integral

Accepted Answer

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

Question 2

The height of a monument is   m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side   meters. Find the volume of the monument.

Accepted Answer

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

Question 3

The volume of the frustum of a pyramid with square base of side b =   , square top of side a =   , and height h =   is   .

Accepted Answer

A) True 
 B)False

Question 4

Find the indefinite integral.

Accepted Answer

A)    
B)          + 8x + C 
C)    
D)          + 8x + C 
A)    
B)          + 8x + C 
C)    
D)          + 8x + C

Question 5

Find the volume of the solid obtained by rotating the region bounded by   about the line

Accepted Answer

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

Question 6

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
y =   , y = 0, x = 2, x = 5; the y-axis

Accepted Answer

The answer of Use the method of cylindrical shells to...

Question 7

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
y = 3x2, y = 0, x = 1; the y-axis

Accepted Answer

Question 8

The base of a solid is the region bounded by the graphs of y = 4 - x2 and y = 0. The cross sections perpendicular to the y-axis are equilateral triangles. Find the volume of the solid.

Accepted Answer

Question 9

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x-axis.

Accepted Answer

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

Question 10

Use a graphing utility to (a) plot the graphs of the given functions and (b) find the x-coordinates of the points of intersection of the curves. Then find an approximation of the area of the region bounded by the curves using the integration capabilities of the graphing utility. Round answers to two decimal places.
y = 3x2, y = 5 - x4

Accepted Answer

a. @#IMG-DLM&

b. –1

Question 11

The velocity v of blood that flows in a blood vessel with radius   and length l at a distance   from the central axis is   where P is the pressure difference between the ends of the vessel and q is the viscosity of the blood. Find the average velocity (with respect to r) over the interval

Accepted Answer

The answer of The velocity v of blood that flows...

Question 12

The tank shown is full of water. Given that water weighs 62.5 lb/ft and R = 5, find the work (in lb-ft) required to pump the water out of the tank.

Accepted Answer

The answer of The tank shown is full of water....

Question 13

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the y-axis. x2 - y2 = 36, x $\ge$ 0, y = -6, y = 6

Accepted Answer

A)  432$\pi$ 
B)  288$\pi$ 
C)  864$\pi$ 
D)  576$\pi$ 
A)  432$\pi$ 
B)  288$\pi$ 
C)  864$\pi$ 
D)  576$\pi$

Question 14

Sketch a plane region, and indicate the axis about which it is revolved so that the resulting solid of revolution has the volume given by the integral.

Accepted Answer

The answer of Sketch a plane region, and indicate the...

Question 15

Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically.

Accepted Answer

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

Question 16

A tank is full of water. Find the work required to pump the water out of the outlet.

Accepted Answer

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

Question 17

If   J of work are needed to stretch a spring from   cm to   cm and another   J are needed to stretch it from   cm to   cm, what is the natural length of the spring? Round the answer to nearest integer.

Accepted Answer

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

Question 18

If   J of work are needed to stretch a spring from 8 cm to 14 cm and another   J are needed to stretch it from 14 cm to 19 cm, what is the natural length of the spring?

Accepted Answer

The answer of If   J of work are...

Question 19

The temperature of a metal rod,   m long, is   x (in degree Celsius) at a distance x meters from one end of the rod. What is the average temperature of the rod?

Accepted Answer

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

Question 20

The height of a monument is   m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side x/4 meters. Find the volume of the monument.

Accepted Answer

The answer of The height of a monument is ...

Evaluate the integral

The height of a monument is m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side meters. Find the volume of the monument.

The volume of the frustum of a pyramid with square base of side b = , square top of side a = , and height h = is .

Find the indefinite integral.

Find the volume of the solid obtained by rotating the region bounded by about the line

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = , y = 0, x = 2, x = 5; the y-axis

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = 3x², y = 0, x = 1; the y-axis

The base of a solid is the region bounded by the graphs of y = 4 - x² and y = 0. The cross sections perpendicular to the y-axis are equilateral triangles. Find the volume of the solid.

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x-axis.

The velocity v of blood that flows in a blood vessel with radius and length l at a distance from the central axis is where P is the pressure difference between the ends of the vessel and q is the viscosity of the blood. Find the average velocity (with respect to r) over the interval

The tank shown is full of water. Given that water weighs 62.5 lb/ft and R = 5, find the work (in lb-ft) required to pump the water out of the tank.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the y-axis. x² - y² = 36, x $\ge$ 0, y = -6, y = 6

Sketch a plane region, and indicate the axis about which it is revolved so that the resulting solid of revolution has the volume given by the integral.

Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically.

A tank is full of water. Find the work required to pump the water out of the outlet.

If J of work are needed to stretch a spring from cm to cm and another J are needed to stretch it from cm to cm, what is the natural length of the spring? Round the answer to nearest integer.

If J of work are needed to stretch a spring from 8 cm to 14 cm and another J are needed to stretch it from 14 cm to 19 cm, what is the natural length of the spring?

The temperature of a metal rod, m long, is x (in degree Celsius) at a distance x meters from one end of the rod. What is the average temperature of the rod?

The height of a monument is m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side x/4 meters. Find the volume of the monument.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 5: Applications of Integration

Evaluate the integral

The height of a monument is m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side meters. Find the volume of the monument.

The volume of the frustum of a pyramid with square base of side b = , square top of side a = , and height h = is .

Find the indefinite integral.

Find the volume of the solid obtained by rotating the region bounded by about the line

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = , y = 0, x = 2, x = 5; the y-axis

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = 3x2, y = 0, x = 1; the y-axis

The base of a solid is the region bounded by the graphs of y = 4 - x2 and y = 0. The cross sections perpendicular to the y-axis are equilateral triangles. Find the volume of the solid.

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x-axis.

The velocity v of blood that flows in a blood vessel with radius and length l at a distance from the central axis is where P is the pressure difference between the ends of the vessel and q is the viscosity of the blood. Find the average velocity (with respect to r) over the interval

The tank shown is full of water. Given that water weighs 62.5 lb/ft and R = 5, find the work (in lb-ft) required to pump the water out of the tank.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the y-axis. x2 - y2 = 36, x ≥\ge≥ 0, y = -6, y = 6

Sketch a plane region, and indicate the axis about which it is revolved so that the resulting solid of revolution has the volume given by the integral.

Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically.

A tank is full of water. Find the work required to pump the water out of the outlet.

If J of work are needed to stretch a spring from cm to cm and another J are needed to stretch it from cm to cm, what is the natural length of the spring? Round the answer to nearest integer.

If J of work are needed to stretch a spring from 8 cm to 14 cm and another J are needed to stretch it from 14 cm to 19 cm, what is the natural length of the spring?

The temperature of a metal rod, m long, is x (in degree Celsius) at a distance x meters from one end of the rod. What is the average temperature of the rod?

The height of a monument is m. A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side x/4 meters. Find the volume of the monument.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = 3x², y = 0, x = 1; the y-axis

The base of a solid is the region bounded by the graphs of y = 4 - x² and y = 0. The cross sections perpendicular to the y-axis are equilateral triangles. Find the volume of the solid.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and inequalities about the y-axis. x² - y² = 36, x $\ge$ 0, y = -6, y = 6