Answer
\[\int_{0}^{1}{\int_{-{{\cos }^{-1}}\left( y \right)}^{{{\cos }^{-1}}\left( y \right)}{f\left( x,y \right)}dxdy}\]
Work Step by Step
\[\begin{align}
& \int_{-\pi /2}^{\pi /2}{\int_{0}^{\cos x}{f\left( x,y \right)}dydx} \\
& \text{Using the graph to switch the order of integration} \\
& -{{\cos }^{-1}}\left( y \right)\le x\le {{\cos }^{-1}}\left( y \right) \\
& 0\le y\le 1 \\
& \text{Then} \\
& \int_{0}^{1}{\int_{-{{\cos }^{-1}}\left( y \right)}^{{{\cos }^{-1}}\left( y \right)}{f\left( x,y \right)}dxdy} \\
\end{align}\]
