Integrating a Function with a Variable and Function Multiplied Together

[wvcaudill2]

Homework Statement

http://img857.imageshack.us/i/no34.jpg/

Homework Equations

The Fundamental Theorem of Calculus, i.e., taking the derivative of an integral yields the original function.

The Attempt at a Solution

I am not sure how to go about integrating this function because I have never had an integral that has both a variable and a function being multiplied together.

 

[Char. Limit]

Try a u-substitution. u=x^2 should work.

 

[wvcaudill2]

Try a u-substitution. u=x^2 should work.

Wow, I can't believe I didnt try u-sub first!

My final answer came to be
$$\frac{f(b^{2})-f(a^{2})}{2}$$

Thanks!