# Thread: solving a double integral

1. ## solving a double integral

int (1/(4-r^2)^0.5) dr dx, r=0 to 2sinx, x=0 to 2pi

I'm stuck at

int (arcsin(sin(x))) dx, x=0 to 2pi

Should i have done a change in variables somewhere?

2. Try plotting the function, and I think you'll see what needs to be done.

3. For x between $-\pi/2$ and $\pi/2$, $arcsin(sin(x))= x$. For x between $\pi/2$ and $3\pi/2$, $arcsin(sin(x))= x- \pi$.

4. I think it's more this:

$\sin^{-1}(\sin(x))=\begin{cases}x,\quad& 0\le x\le\pi/2\\