Hi guys,

I'm a tad stuck on this problem.

First a sketch of the region:Let be the region in enclosed in the circle and below the line

Calculate the integral by order of integration

So I figured I could break it up into 2 regions, the triangular area under and one quarter of the circle which I can multiply by 3 to give me the total area of all 3 quarters.

My problem arises when trying to integrate the quarter of the circle.

I've set to transform the integral to:

Which then by recursive use of the reduction formula gives me an answer of which isn't correct since it should be

Where did I go wrong on this? Also, this question is only worth about 4 marks, and in my opinion my method is too much trouble for only 4 marks. What am I missing?

All help appreciated.