Question

高等数学在线求解，定积分与反常积分（易）？

要过程有解答

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Answer 1

（1） I = ∫<1,+∞>dx/x^2 = [-1/x]<1,+∞> = 0 +1 = 1
(2) I = ∫<1,+∞>e^(-100x)dx = (-1/100)∫<1,+∞>e^(-100x)d(-100x)
= (-1/100)[e^(-100x)]<1,+∞> = (-1/100)[0-e^(-100)] = 1/(100e^100)
(3) 令 √(5-4x) = u, 则 x = (5-u^2)/4, dx = (-1/2)udu,
I = ∫<-1, 1>dx/√(5-4x) = ∫<3, 1>(-1/2)udu/u = (-1/2)(1-3) = 1
(4) 奇函数 在对称区间上定积分为 0， 故得 I = 0