方法1：因为积分值只与被积函数和积分域有关，与积分变量无关，所以 \[I^{2}=\left ( \int_{0}^{\infty }e^{-x^{2}}\mathrm{d}x \right ...

问题：设\(\displaystyle f\left( x,y \right)\)是定义在区域\(\displaystyle 0\leqslant x\leqslant 1\)，\(\displays ...