求二重积分∫(0,2)dx∫(x,2)e^(-y^2)dy

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)