# An integration problem which is supposed to be easy

1. Jan 22, 2010

### kyva1929

http://img686.imageshack.us/img686/7320/clipboard01by.png [Broken]

I am just lost at how to use the given information to find out the required integral. I've tried fundamental theorem of calculus, substitution, and integration by parts, but they do not seem to work for me.

Thank you!

Last edited by a moderator: May 4, 2017
2. Jan 22, 2010

### Dick

Sure. Use the fundamental theorem in the form of the Liebniz integral rule. Then look for something to integrate by parts.

3. Jan 22, 2010

### Dick

Actually, I think it's even easier if you change the integration variable to u=x-t. THEN apply the fundamental theorem.

4. Jan 22, 2010

### kyva1929

Using u=x-t, du=-dt, and the integral becomes -(x-u)*f(u) du integrating from x to 0, but now I am not sure how it could be integrated to some useful form relating it to 1-cos(x) ?

5. Jan 22, 2010

### Dick

Your u integral is equal to 1-cos(x). Now differentiate both sides.

6. Jan 22, 2010

### kyva1929

I got it, thank you very much!