Are these equations correct?

[Micko]

Hello to all,
I'm solving one interesting problem that basically tailor to the problem in attachment.
I'm pretty much sure I'm on the right track, but my knowledge of math became little rusty since colledge, so I need to ask fo confirmation.
Please have a look and tell me if I wrote these equation correctly.

Thank you

 

[vishal_garg]

ya you are goin the right way...

 

[Micko]

ya you are goin the right way...

Thank you, I was sure I'm on the right track. However I got integrals which are not so complicated but solution is rather complicated (arcsin and similar). I wondew if problem is easier with cilindrical coordinates...

 

[ice109]

hint: k=rcos[theta] is the equation of a circle polar coordinates