Teacher needs help with polar co-ordinates
Haha. I bet this will be one of the more unusual questions you get on here. I am a trainee teacher and I noticed last week that one of the other teachers was asked a question about polar co-ordinates. He couldn't do it, and after showing it to the rest of us in the staffroom, we decided we couldn't either! Any help or guidance you could give would be very appreciated. By next week the student will probably be on the next chapter, but for the sake of our sanity we would like to see how to do it!
The question is:
Integrate (a^2) / (1 + cos theta) between 0 and pi/2 where a is just a constant.
Now we know that an integration in polar co-ordinates is
A = (a^2) / 2 x integral 1 / (1+cos theta)^2 d-theta
Everything we try from there onwards just makes things much worse. Substitution doesn't help, so I was thinking there could be some trig-identity which would make things easier but I couldn't see one.