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?
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Try plotting the function, and I think you'll see what needs to be done.
For x between $\displaystyle -\pi/2$ and $\displaystyle \pi/2$, $\displaystyle arcsin(sin(x))= x$. For x between $\displaystyle \pi/2$ and $\displaystyle 3\pi/2$, $\displaystyle arcsin(sin(x))= x- \pi$.
I think it's more this: $\displaystyle \sin^{-1}(\sin(x))=\begin{cases}x,\quad& 0\le x\le\pi/2\\ \pi-x,\quad& \pi/2\le x\le 3\pi/2\\ x-2\pi,\quad& 3\pi/2\le x\le 2\pi\end{cases}.$
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