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.