Exam 7: Techniques of Integration

A manufacturer of light bulbs wants to produce bulbs that last about hours but, of course, some bulbs burn out faster than others. Let be the fraction of the company's bulbs that burn out before t hours. lies between 0 and 1. Let . What is the value of ?

Evaluate the integral.

The region under the graph of on the interval [1, 2] is revolved about the x-axis. Find the volume of the resulting solid.

Evaluate the integral.

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Evaluate the integral.

Evaluate the integral.

Find the area of the region bounded by the hyperbola and the line .

Find the integral.

Evaluate the integral.

Use the Table of Integrals to evaluate the integral.

For what values of K is the following integral improper?

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Find the integral using an appropriate trigonometric substitution.

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

Evaluate the integral.

Find the integral.

Use a table of integrals to evaluate the integral.

Find the integral.

Use a table of integrals to evaluate the integral.