求∫(0,1)e^√x dx

题目

求∫(0,1)e^√x dx

答案

令：√x = t ,则：x = t^2 ; dx = 2tdt
∫(0,1) e^√x dx
=∫(0,1) e^t (2tdt)
= 2 ∫(0,1) tde^t
= 2 [ te^t|(0,1) -∫(0,1) e^t dt ]
= 2 [ (e-0) - e^t|(0,1) ]
= 2 [ e - (e-1) ]
= 2