高等数学3道题求推导过程

3道高等数学题 求推导过程 具体过程
2025-05-22 16:10:27
推荐回答(2个)
回答1:

72. ∫<1, +∞> dx/x^4 =∫<1, +∞> x^(-4)dx = -(1/3)[1/x^3]<1, +∞> = 1/3
62. ∫<-π, π>xsinxdx = 2∫<0, π>xsinxdx = -2∫<0, π>xdcosx
= -2[xcosx]<0, π> + 2∫<0, π>cosxdx
= 2π + 2[sinx]<0, π> = 2π
36. ∫<0, 2>|1-x|dx = ∫<0, 1>(1-x)dx + ∫<1, 2>(x-1)dx
= [x-x^2/2]<0, 1> + [x^2/2-x]<1, 2> = 1/2 + 1/2 = 1

回答2: