求二重积分∫(0,2)dx∫(x,2)e^(-y^2)dy

2025-01-01 07:49:21
推荐回答(2个)
回答1:

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)

回答2:

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