求e的根号下x次幂的定积分，区间为0-1

Question

如题所述

Answer 1

let
y=√x
dy = dx/(2√x)
dx = 2y dy
x=0, y=0
x=1, y=1

∫(0->1) e^(√x) dx
=∫(0->1) 2ye^y .dy
=2∫(0->1) y de^y
=2[y.e^y]|(0->1) -2∫(0->1) e^y dy
=2e - 2[e^y]|(0->1)
=2e -(2e-2)
=2本回答被提问者采纳