求二重积分∫(0,2)dx∫(x,2)e^(-y^2)dy
问题描述：
求二重积分∫(0,2)dx∫(x,2)e^(-y^2)dy
答
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答
交换积分次序：∫(0,2)dx∫(x,2)e^(-y²)dy=∫(0,2)dy∫(0,y)e^(-y²)dx=∫(0,2) ye^(-y²)dy=(1/2)∫(0,2) e^(-y²)d(y²)=(-1/2)e^(-y²) |(0,2)=(1/2)(1-e⁻⁴)