求∫(0,1)e^√x dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/26 11:11:43
求∫(0,1)e^√xdx求∫(0,1)e^√xdx求∫(0,1)e^√xdx令:√x=t;x=t^2;dx=2tdt∫(0,1)e^√xdx=∫(0,1)e^t(2tdt)=2∫(0,1)tde^t

求∫(0,1)e^√x dx
求∫(0,1)e^√x dx

求∫(0,1)e^√x dx
令:√x = t ; 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

e-1