Exam 6: Applications of the Definite Integral

Pick the integral that represents a volume calculation by cylindrical shells that is equivalent to the following integral that represents a calculation of the same volume but by the method of washers.

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about x = 3.

A 0.5 kg rock is dropped from the edge of a 17-foot cliff. How fast will it be going when it hits the ground at the base of the cliff?

A solid shape described as the region bounded by revolved around the y-axis, needs to have 1/4 of its volume trimmed off to meet a weight restriction. This will be done by reducing the radius of the piece - in other words, the resulting shape will be described as above, but with the region also bounded by x = q. Find the resulting radius, q.

Find the volume of the solid formed by revolving the region bounded by about x = 4.

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about y = 10.

Find the mean of the random variable with the given pdf.

Find the area between the following curves on the given interval.

Estimate the intersection points to the nearest tenth then use these points to estimate the area.

Use the best method available to find the volume of the solid formed by revolving the region bounded by and about the y-axis. Write the integral that is used to find the volume.

Identify the integral used to determine the surface area of the surface of revolution for the shape described by , , revolved about the x-axis.

Use Simpson's rule to estimate the volume from the given cross sectional areas.

The pdf describing the chance that a given insect will die at a particular age, x days, is . What is the chance the insect will live less than 10 days?