Exam 8: Techniques of Integration

Evaluate the following improper integrals. A) B)

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods. A) B) . (Hint: Use .

Evaluate the integral .

Calculate the following integral using reduction formulas as necessary.

Use substitution and reduction formulas to evaluate the integral .

Evaluate the following integrals. A) B)

Evaluate .

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

Calculate and for the following. A) B)

Which two of the following integrals converge? A) B) C) D)

Evaluate the following integral using trigonometric identities and reduction formulas.

Calculate the following integral in terms of inverse hyperbolic functions.

Evaluate the integral .

Evaluate .

The partial fraction decomposition of is:

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

Evaluate the integral .

To evaluate the integral using Integration by Parts, we should choose:

Use the substitution and the identities and to evaluate the integral .

Evaluate the integral .