Exam 8: Techniques of Integration

Evaluate the integral

Evaluate .

Use the error bound to find a value of for which in approximating the integral .

To show that converges, we should use:

Calculate the following integral in terms of inverse hyperbolic functions.

Verify that has a removable discontinuity at , define so that is continuous at and estimate by .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Verify that has a removable discontinuity at , define so that is continuous at 0, and estimate by .

Verify that is a probability density function on and calculate its mean value.

Evaluate the integral .

Evaluate .

To evaluate the integral using integration by parts, the convenient choice is :

Find a constant such that is a probability density on the interval and compute the probability .

Calculate the following integrals using the reduction formulas when necessary. A) B)

Approximate the volume of the solid obtained by rotating the graph of from about the line by using .

To evaluate the integral by Integration by Parts, the convenient choice is

Calculate the integral .

Evaluate the integral .