Double Integral - Weird Region
The function I have is
I want to integrate over this region. So I noticed its symmetric first of all. So my plan is to only consider the positive half first and then double the resulting area I find. Secondly I find that I can separate this region into 2 regions. (See attached image)
Region 1: A triangle with base = height = .
Region 2: upper limit of y is arc created by and lower limit is . And x ranges from 0 to .
I find when I go to do the double integral for region 2 I keep getting a negative answer.
The integral for region 2 I'm tyring is:
Any suggestions? Am I on the right track? Or completely off?
Thanks in advance.