设f(x)=∫(1,x^2) e^(-t)/t d

设f(x)=∫(1,x^2) e^(-t)/t dt,求∫(0,1)xf（x）dt

4个回答

f(x) = ∫(1→x²) e^(- t)/t dt
f'(x) = 2x · e^(- x²)/x² = 2e^(- x²)/x
f(1) = 0,∵上限 = 下限
∫(0→1) xf(x) dx = ∫(0→1) f(x) d(x²/2)
= (1/2)x²f(x)：(0→1) - (1/2)∫(0→1) x² · f'(x) dx