Integrate $\iint_D\exp\{\min(x^2, y^2)\}\mathrm{d}x\mathrm{d}y$ Compute the integral:
\begin{equation}
\iint\limits_{\substack{\displaystyle 0 \leqslant x \leqslant 1\\\displaystyle 0 \leqslant y \leqslant 1}}\exp\left\{\min(x^2, y^2)\right\}\mathrm{d}x\mathrm{d}y
\end{equation}
$D$ is the rectangle with vertices $(0,0)$, $(0,1)$, $(1,0)$ and $(1,1)$ and $\min(x^2,y^2)$ is the minimum of the numbers $x^2$ and $y^2$.
I dont have a clue about how I can integrate this function. I thought of using Taylor series but I am not sure if this would work either. Can anyone help me out?

Hint: Split $D$ into two triangles, according to $x\ge y$ or $y\ge x$, and calculate both integrals on these triangles.
