Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

omg you are correct.

Answer 5

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

Answer 6

yw

Answer 7

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

Answer 8

can't I do substitution

Answer 9

you can try

Answer 10

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

Answer 11

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

Answer 12

there exacly you example

Answer 13

your*

Answer 14

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