How to Correctly Use Substitution for Polar Coordinates in Integrals?

[Qyzren]

http://img187.imageshack.us/my.php?image=polargy3.jpg

The Attempt at a Solution

http://img484.imageshack.us/my.php?image=picture155jy1.jpg
i get an extra cos² thi term! WHY!
am i doing the substitution completely wrong?? or i forgot/left something out which i can not seem to see!

Thank you

 

[Gib Z]

4th line, $dw_1= -w\sin \phi d\phi$ unfortunately :(

 

[Qyzren]

oops, i meant to write dw1 = cos thi dw.
nevermind, i got it.
I have to use Jacobian matrix instead of what i did.