求下列函数的定积分 (1) ∫(0.2) (e^2x +x^-1)dx (2) ∫(0.π/2) sin^2 x/2 dx

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求下列函数的定积分(1)∫(0.2)(e^2x+x^-1)dx(2)∫(0.π/2)sin^2x/2dx求下列函数的定积分(1)∫(0.2)(e^2x+x^-1)dx(2)∫(0.π/2)sin^2x

求下列函数的定积分 (1) ∫(0.2) (e^2x +x^-1)dx (2) ∫(0.π/2) sin^2 x/2 dx
求下列函数的定积分 (1) ∫(0.2) (e^2x +x^-1)dx (2) ∫(0.π/2) sin^2 x/2 dx

求下列函数的定积分 (1) ∫(0.2) (e^2x +x^-1)dx (2) ∫(0.π/2) sin^2 x/2 dx
∫(0->2) (e^2x + 1/x) dx
= (1/2)e^2x + lnx:(0->2)
= (1/2)e^4 + ln2 - (1/2*1 + ln0)
= (1/2)e^4 + ln2 - 1/2 + ln0,由于ln0趋向负无穷大
∴这个积分发散
∫(0->π/2) sin²(x/2) dx
= (1/2)∫ (1-cosx) dx
= (1/2)(x - sinx):(0->π/2)
= (1/2)[π/2 - sin(π/2)] - (1/2)(0 - sin0)
= (1/2)(π/2 - 1)
= π/4 - 1/2