Question 1

Find the coordinates of the centroid for the region bounded by the curves   , x = 0,
and y =   .

Accepted Answer

The answer of Find the coordinates of the centroid for...

Question 2

Find the centroid of the region shown, not by integration, but by locating the centroids of the
rectangles and triangles and using additivity of moments.

Accepted Answer

The answer of Find the centroid of the region shown,...

Question 3

A cylindrical drum of diameter 2 ft and length 6 ft is lying on its side, submerged in water 16 ft deep. Find the force exerted by the water on one end of the drum to the nearest pound. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

2941

Question 4

Find the arc length function for the curve   with starting point   .

Accepted Answer

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

Question 5

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of   per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and   th weeks of summer?

Accepted Answer

A) 5702 
B) 6702 
C) 8702 
D) 7702 
E)    
A) 5702 
B) 6702 
C) 8702 
D) 7702 
E)

Question 6

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 7

Boxes are labeled as containing 500 g of cereal. The machine filling the boxes produces weights that are normally distributed with standard deviation 12
g.If the target weight is 500 g, what is the probability that the machine produces a box with less than   g of cereal? Round your answer to four decimal places.

Accepted Answer

The answer of Boxes are labeled as containing 500 g...

Question 8

Use the arc length formula to find the length of the curve.

Accepted Answer

The answer of Use the arc length formula to find...

Question 9

Find the area of the surface obtained by revolving the given curve about the x-axis.   on

Accepted Answer

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

Question 10

If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 195 and   .

Accepted Answer

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

Question 11

Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer to four decimal places.   P (3, 12), Q (3.2, 13.24)

Accepted Answer

A) 2.4331 
B) 1.2166 
C) 3.6497 
D) 6.0828 
A) 2.4331 
B) 1.2166 
C) 3.6497 
D) 6.0828

Question 12

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

Question 13

The standard deviation for a random variable with probability density function f and mean µ is defined   . Find the standard deviation for an exponential density function with mean   .

Accepted Answer

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

Question 14

The marginal cost function   is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is   (measured in dollars per unit) and the fixed start-up cost is   , use the Total Change Theorem to find the cost of producing the first 5,000 units.

Accepted Answer

A) $35,444,500 
B) $   
C) $35,434,500 
D) $35,454,500 
E) $35,484,500 
A) $35,444,500 
B) $   
C) $35,434,500 
D) $35,454,500 
E) $35,484,500

Question 15

Find the length of the curve.

Accepted Answer

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

Question 16

Find the centroid of the region bounded by the graphs of the given equations.

Accepted Answer

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

Question 17

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) 208 lb 
B) 104 lb 
C) 1040 lb 
D) 520 lb 
A) 208 lb 
B) 104 lb 
C) 1040 lb 
D) 520 lb

Question 18

The demand function for a commodity is given by   . Find the consumer surplus when the sales level is   .

Accepted Answer

A) $9458 
B) $10458 
C) $   
D) $8458 
E) $4458 
A) $9458 
B) $10458 
C) $   
D) $8458 
E) $4458

Question 19

A trough is filled with a liquid of density 855 kg/   . The ends of the trough are equilateral triangles with sides   m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

Accepted Answer

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

Question 20

Find the length of the curve.

Accepted Answer

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

Find the coordinates of the centroid for the region bounded by the curves , x = 0, and y = .

Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles and using additivity of moments.

A cylindrical drum of diameter 2 ft and length 6 ft is lying on its side, submerged in water 16 ft deep. Find the force exerted by the water on one end of the drum to the nearest pound. (The weight density of water is 62.4 lb/ft³.)

Find the arc length function for the curve with starting point .

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and th weeks of summer?

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

Use the arc length formula to find the length of the curve.

Find the area of the surface obtained by revolving the given curve about the x-axis. on

If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 195 and .

Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer to four decimal places. P (3, 12), Q (3.2, 13.24)

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

The standard deviation for a random variable with probability density function f and mean µ is defined . Find the standard deviation for an exponential density function with mean .

The marginal cost function is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is (measured in dollars per unit) and the fixed start-up cost is , use the Total Change Theorem to find the cost of producing the first 5,000 units.

Find the length of the curve.

Find the centroid of the region bounded by the graphs of the given equations.

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.)

The demand function for a commodity is given by . Find the consumer surplus when the sales level is .

A trough is filled with a liquid of density 855 kg/ . The ends of the trough are equilateral triangles with sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

Find the length of the curve.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques 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 8: Further Applications of Integration

Find the coordinates of the centroid for the region bounded by the curves , x = 0, and y = .

Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles and using additivity of moments.

A cylindrical drum of diameter 2 ft and length 6 ft is lying on its side, submerged in water 16 ft deep. Find the force exerted by the water on one end of the drum to the nearest pound. (The weight density of water is 62.4 lb/ft3.)

Find the arc length function for the curve with starting point .

A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of mosquitoes is increasing at an estimated rate of per week (where t is measured in weeks). By how much does the mosquito population increase between the 4th and th weeks of summer?

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

Use the arc length formula to find the length of the curve.

Find the area of the surface obtained by revolving the given curve about the x-axis. on

If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 195 and .

Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer to four decimal places. P (3, 12), Q (3.2, 13.24)

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

The standard deviation for a random variable with probability density function f and mean µ is defined . Find the standard deviation for an exponential density function with mean .

The marginal cost function is defined to be the derivative of the cost function. If the marginal cost of manufacturing x units of a product is (measured in dollars per unit) and the fixed start-up cost is , use the Total Change Theorem to find the cost of producing the first 5,000 units.

Find the length of the curve.

Find the centroid of the region bounded by the graphs of the given equations.

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.)

The demand function for a commodity is given by . Find the consumer surplus when the sales level is .

A trough is filled with a liquid of density 855 kg/ . The ends of the trough are equilateral triangles with sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.

Find the length of the curve.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques 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

A cylindrical drum of diameter 2 ft and length 6 ft is lying on its side, submerged in water 16 ft deep. Find the force exerted by the water on one end of the drum to the nearest pound. (The weight density of water is 62.4 lb/ft³.)

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.)