Exam 8: Further Applications of Integration

Find the length of the curve for the interval

Select the correct Answer for each question. -Find the area of the surface obtained by rotating the circle about the line

A large tank is designed with ends in the shape of the region between the curves and measured in feet.Find the hydrostatic force on one end of the tank if it is filled to a depth of ft with gasoline.(Assume that the density of the gasoline is

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

Find the coordinates of the centroid for the region bounded by the curves and

A type of lightbulb is labeled as having an average lifetime of It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean What is the median lifetime of these lightbulbs? Give yourAnswer rounded to two decimal places.

Find the length of the curve.Select the correct Answer

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2 minutes.The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger.But she doesn't want to give away free hamburgers to more than f her customers.What value of x must she use in the advertisement "if you aren't served within minutes, you get a free hamburger"?

Select the correct Answer for each question. -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.

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 )

Select the correct Answer for each question. -Find the arc length of the graph of the given equation on the specified interval.y =

Select the correct Answer for each question. -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 )

Select the correct Answer for each question. -Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the graphs of and about the y-axis.

Find the coordinates of the centroid for the region bounded by the curves , and

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

Find the center of mass of the system comprising masses located at the points in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters.

Let the function whose graph is shown be a probability density function.Calculate the mean.

Select the correct Answer for each question. -Find the length of the curve.

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

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