## anonymous 3 years ago Evaluate ∫∫ over D (cos(sqrt(x^2+y^2)) dA by changing polar coordinates where the disk is with center of origin and radius 2

1. anonymous

I got up to ∫∫[0 to 2pi] [0 to 2] cos(sqrt(r)) r dr dt

2. anonymous

but I can't solve for it! How do integrate r*cos(sqrt(r))

3. anonymous

$\int\limits\int\limits_{D}=\int\limits_{0}^{2\pi} d\theta\ \int\limits_{0}^{2}r \cos rdr$

4. anonymous

omg you are correct.

5. anonymous

spent literally 30 mins trying to see what I did wrong. That was quick thanks a lot man

6. anonymous

yw

7. anonymous

by the way:int( rcos r) it's done by integration by parts

8. anonymous

can't I do substitution

9. anonymous

you can try

10. anonymous

haha I just did and it didn't work, alright thanks again!

11. anonymous

if you have problems look here, :) http://en.wikipedia.org/wiki/Integration_by_parts

12. anonymous

there exacly you example

13. anonymous

your*

14. anonymous

Yeah I got it now, thanks a lot for your help!