Problem

Part II Fill in the blanks

13. If $a$ and $b$ are positive constants and if $\max\{p,q\}$ denotes the maximum between the numbers $p$ and $q$, the iterated integral

$$\int_{0}^{a}\int_{0}^{b} e^{\max\{b^2x^2,a^2y^2\}}\,dy\,dx=\underline{\quad(17)\quad}.$$