Question

高等数学问题 计算积分上限正无穷,下限0, x(e^-k(x^2))dx

Answer 1

∫(0→+∞)x(e^-k(x^2))dx
=0.5∫(0→+∞)(e^-k(x^2))d(x^2)
设t=x^2
=0.5∫(0→+∞)(e^-kt)dt
=-(1/2k) (e^-kt) (0→+∞)
=1/2k