计算积分∫(0,2)dx∫(x,2)e^(-y²)dy
人气:312 ℃ 时间:2020-03-25 06:29:49
解答
把积分区域D画图,改换积分次序:
∫(0~1)dx∫(x~1)e^(-y^2)dy
=∫(0~1)dy∫(0~y)e^(-y^2)dx
=∫(0~1) ye^(-y^2)dy 被积函数的原函数是-1/2e^(-y^2)
=1/2×(1-1/e)
=(e-1)/(2e)
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