Exam 8: Further Applications of Integration

Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis. y-axis

Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the x-axis on the interval .

Find the exact coordinates of the centroid.

For the following exercise, (a) plot the graph of the function f, (b) write an integral giving the arc length of the graph of the function over the indicated interval, and (c) find the arc length of the curve accurate to two decimal places. = x - ; [0, 6]

A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft³.) (ft)

A steady wind blows a kite due west. The kite's height above ground from horizontal position to ft is given by . Find the distance traveled by the kite. Give your answer rounded to two decimal places.

Find the centroid of the region bounded by the graphs of and .

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

Find the centroid of the region shown in the figure.

Let a) For what value of c is f a probability density function? b) For that value of c, find P (-1 < X < 1).

Find the centroid of the region bounded by the curves.

A movie theater has been charging $ .00 per person and selling about tickets on a typical weeknight. After surveying their customers, the theater estimates that for every $ that they lower the price, the number of moviegoers will increase by per night. Find the demand function and calculate the consumer surplus when the tickets are priced at $ .

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

A demand curve is given by . Find the consumer surplus when the selling price is $ .

Find the area of the surface obtained by rotating the circle about the line .

Find the area of the surface obtained by revolving the given curve about the y-axis. x = on [0, 2]

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

Find the length of the curve for the interval .

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

Use Simpson's Rule with n = 6 to estimate the length of the curve , . Round your answer to six decimal places.