So I'm working on some multivariable calculus homework, and I can't seem to figure out why my professor takes this particular approach to the solution...
The Question: $$ S = \{(x,y) \in R^2: 0 \leq x \leq 1, 0 \leq y \leq sin^{-1}x\} $$ And we have to evaluate $\int \int_{S} dA $
My professor's approach to this problem involves changing the integral bounds, so instead of the double integral setup looking like: $\int_{0}^{1} \int_{0}^{sin^{-1}}dydx$, it looks like $\int_{0}^{\pi/2} \int_{sin(y)}^{1}dxdy$
Can someone please explain how he got to this rearranged integral bounds setup, and additionally is there a general process for rewriting the integral bounds for a double integral?
Here's two drawings that hopefully will be helpful for you.