0到e 的定积分e ^√x
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0到e 的定积分e ^√x
![0到e 的定积分e ^√x](/uploads/image/z/7381573-61-3.jpg?t=0%E5%88%B0e+%E7%9A%84%E5%AE%9A%E7%A7%AF%E5%88%86e+%5E%E2%88%9Ax)
令√x=t,x=t^2,dx=2tdt.
故S(0,e)e^√xdx
=S(0,√e)e^t *2tdt
=2S(0,√e)td(e^t)
=2[te^t(0,√e)-S(0,√e)e^tdt ]
=2[(t-1)e^t](0,√e)
=2[(√e-1)e^(√e)]+2e^(√e)
=2√e*e^(√e)
=2e^[(√e)+1/2]
故S(0,e)e^√xdx
=S(0,√e)e^t *2tdt
=2S(0,√e)td(e^t)
=2[te^t(0,√e)-S(0,√e)e^tdt ]
=2[(t-1)e^t](0,√e)
=2[(√e-1)e^(√e)]+2e^(√e)
=2√e*e^(√e)
=2e^[(√e)+1/2]