Note: You can get full credit for this problem by just entering the final answer (to the last question) correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit.

Consider the definite integral
The first step in evaluating this integral is to apply integration by parts: where
=
and where =
Note: Use for .

After integrating by parts, we obtain the integral on the right hand side where
=
The most appropriate substitution to simplify this integral is where
=

Note: We are using as variable for angles instead of , since there is no standard way to type on a computer keyboard.

After making this substitution and simplifying (using trig identities), we obtain the integral where
=
=
=
After evaluating this integral and plugging back into the integration by parts formula we obtain:
=

You can earn full credit by answering just the last part.