I'm normally ok with these types of questions but this one has got me really stuck. I tried converting to polar coordinates but it gave a horrible integration to carry out for me so I think I've done it wrong. So yeah, any help appreciated .
I couldn't write out the integral on here so I've attached the paper that the question's from (it wouldnt let me attach a JPEG or GIF of the question - why?!). Question 10 .
Ahh whoops! Ok, so I checked and I had made a stupid mistake but I carried on with in the integrand and converted to polars
but I ended up with
which I'm pretty sure must be wrong. I'm not sure if I'm just being stupid or if I've been awake too long but if you can see where I've gone wrong, could you point it out for me? Thanks!
What I can tell you is that after you convert to polar coordinates you will have a double integral of the from
In you integrate with respect to theta first you should end up with
I just can't get that I don't know where I'm going wrong either!
Ok so changing to polar coordinates I get
in the integrand but I just can't integrate all the sine and cosines when integrating with respect to . Am I doing the change to polar coordinates wrong or something?