Ive changed it too:

c) http://bildr.no/view/393338 r) http://bildr.no/view/393339

c) http://bildr.no/view/393340  r)     http://bildr.no/view/393345    http://bildr.no/view/393342  

http://bildr.no/view/393351

I tried to write in ordinart text instead of just copy it like an image above and if I would it would be something like:

evalf(int(int(int(f(r,theta),r=1/sin(2*theta)*cos(theta)..2*sin(theta)),theta=Pi/8..Pi/2))

 I dont understand why r nr. 2 gives a function with variables and not a number?

Sorry I meant to write sin(2theta)

By cos^2(theta) I meant cos(theta))^2

rcos does not mean anything without theta

By numerical evaluation do you mean evalf. This is what I got when I used evalf to calculate with polar coordinates and with cartesian coordinates. There is one link for every command and result:

c)http://bildr.no/view/391457  r) http://bildr.no/view/391458

c)http://bildr.no/view/391459 r) http://bildr.no/view/391460

c) http://bildr.no/view/391463  r) http://bildr.no/view/391465

c) http://bildr.no/view/391470 r) http://bildr.no/view/391471

From the last c and r you can see that with cartesian cooerdinates you get an definite answer.

From the second c og r you can see the answer I got from polar coordinates. The problem seems to me to be that theta is not calculated