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integrating in polar co-ordinates

Hi,

Just wondering if someone could please have a look at my working for the question i am currently working on. I got a bit of help from CaptainBlack on this forum about a week or so about how to approch the problem and this is what i have come up with so far. I was reading through my notes and noticed they talk of and use a factor called the jacobian. does this factor have to be used everytime you integrate in polar co-ordinates? If so how would i apply it to this problem. I get a negative for my answer which is not what i was expecting.

Thanks

Elbarto