Exam 8: Further Applications of Integration

A trough has vertical ends that are equilateral triangles with sides of length 7 ft.If the trough is filled with water to a depth of 4 ft, find the force exerted by the water on one end of the trough.Round to one decimal place.(The weight density of water is

Find the length of the line segment joining the two given points by finding the equation of the line using Equation (2).Then check yourAnswer by using the distance formula.Select the correct Answer(0, 0), (4, 6)

Select the correct Answer: for each question. -The demand function for a commodity is given by Find the consumer surplus when the sales level is

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

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

Write an integral giving the area of the surface obtained by revolving the curve about the x-axis.(Do not evaluate the integral.) on [4, 6]

Select the correct Answer: for each question. -Write an integral giving the area of the surface obtained by revolving the curve about the x-axis.(Do not evaluate the integral.)

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

Find the centroid of the region bounded by the given curves.Select the correct Answer

Find the area of the surface obtained by rotating the curve about the

Find the area of the surface obtained by revolving the given curve about the

Find the area of the surface obtained by rotating the circle about the line Select the correct Answer

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

An aquarium is 3 ft long, 2 ft wide, and 2 ft deep.If the aquarium is filled with water, find the force exerted by the water (a) on the bottom of the aquarium, (b) on the longer side of the aquarium, and (c) on the shorter side of the aquarium.(The weight density of water is )

Find the length of the curve.Select the correct Answer

Find the arc length of the graph of the given equation on the specified interval.

Select the correct Answer for each question. -If 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

a) For what value of is a probability density function? b) For that value of find

Select the correct Answer: for each question. -Find the centroid of the region bounded by the given curves.

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