Question 1

Find the volume common to two spheres, each with radius r =   if the center of each sphere lies on the surface of the other sphere.

Accepted Answer

The answer of Find the volume common to two spheres,...

Question 2

Calculate the center of mass of the lamina with density   =   .

Accepted Answer

The answer of Calculate the center of mass of the...

Question 3

Find the area of the shaded region.

Accepted Answer

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

Question 4

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of   ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/   .)

Accepted Answer

The answer of A swimming pool is 10 ft wide...

Question 5

Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.

Accepted Answer

The answer of Racing cars driven by Chris and Kelly...

Question 6

The base of S is a circular region with boundary curve   Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base.Find the volume of S.

Accepted Answer

The answer of The base of S is a circular...

Question 7

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

A) 332.8 lb 
B) 1331.2 lb 
C) 2662.4 lb 
D) 665.6 lb 
A) 332.8 lb 
B) 1331.2 lb 
C) 2662.4 lb 
D) 665.6 lb

Question 8

Set up, but do not evaluate, an integral for the length of the curve.

Accepted Answer

The answer of Set up, but do not evaluate, an...

Question 9

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

Accepted Answer

A) 3.141257 
B) 91.504 
C) 18.3008 
D) 12.08127 
E) 3.66016 
A) 3.141257 
B) 91.504 
C) 18.3008 
D) 12.08127 
E) 3.66016

Question 10

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

Accepted Answer

The answer of Find the volume of the solid obtained...

Question 11

Find the volume of a pyramid with height   and base an equilateral triangle with side a =   .

Accepted Answer

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

Question 12

Solve the differential equation.

Accepted Answer

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

Question 13

Find the area of the surface obtained by rotating the curve about the   -axis.

Accepted Answer

The answer of Find the area of the surface obtained...

Question 14

Find the center of mass of a lamina in the shape of a quarter-circle with radius   with density   =   .

Accepted Answer

The answer of Find the center of mass of a...

Question 15

A tank contains   L of brine with   kg of dissolved salt. Pure water enters the tank at a rate of   L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after   minutes?

Accepted Answer

The answer of A tank contains   L of...

Question 16

Sketch the region enclosed by   Find the area of the region.

Accepted Answer

The answer of Sketch the region enclosed by  ...

Question 17

Find the length of the curve.

Accepted Answer

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

Question 18

Find the volume of a cap of a sphere with radius r =   and height h = 3   .

Accepted Answer

The answer of Find the volume of a cap of...

Question 19

Find the area of the surface obtained by rotating the curve about the x-axis.

Accepted Answer

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

Question 20

Find the centroid of the region bounded by the given curves.

Accepted Answer

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

Find the volume common to two spheres, each with radius r = if the center of each sphere lies on the surface of the other sphere.

Calculate the center of mass of the lamina with density = .

Find the area of the shaded region.

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .)

Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.

The base of S is a circular region with boundary curve Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base.Find the volume of S.

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)

Set up, but do not evaluate, an integral for the length of the curve.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

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

Find the volume of a pyramid with height and base an equilateral triangle with side a = .

Solve the differential equation.

Find the area of the surface obtained by rotating the curve about the -axis.

Find the center of mass of a lamina in the shape of a quarter-circle with radius with density = .

A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes?

Sketch the region enclosed by Find the area of the region.

Find the length of the curve.

Find the volume of a cap of a sphere with radius r = and height h = 3 .

Find the area of the surface obtained by rotating the curve about the x-axis.

Find the centroid of the region bounded by the given curves.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 7: Applications of Integration

Find the volume common to two spheres, each with radius r = if the center of each sphere lies on the surface of the other sphere.

Calculate the center of mass of the lamina with density = .

Find the area of the shaded region.

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .)

Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midpoint Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.

The base of S is a circular region with boundary curve Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base.Find the volume of S.

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Set up, but do not evaluate, an integral for the length of the curve.

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

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

Find the volume of a pyramid with height and base an equilateral triangle with side a = .

Solve the differential equation.

Find the area of the surface obtained by rotating the curve about the -axis.

Find the center of mass of a lamina in the shape of a quarter-circle with radius with density = .

A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes?

Sketch the region enclosed by Find the area of the region.

Find the length of the curve.

Find the volume of a cap of a sphere with radius r = and height h = 3 .

Find the area of the surface obtained by rotating the curve about the x-axis.

Find the centroid of the region bounded by the given curves.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)