Problem

乙、計算、證明題：共 3 題，每題 12 分，共 36 分。須詳細寫出計算及證明過程，否則不予計分。

1. Sketch the region of integration, reverse the order of integration, and evaluate the integral $\displaystyle\int_0^3\int_{\sqrt{x/3}}^1 e^{y^3}\,dy\,dx$.