求定积分,积分0到1,xe的x^2次方dx

问题描述:

求定积分,积分0到1,xe的x^2次方dx

∫(0→1) xe^x² dx
= ∫(0→1) e^x² d(x²/2)
= (1/2)[e^x²] |(0,1)
= (1/2)(e^1 - e^0)
= (e - 1)/2

∫xe^(x^2)dx
=(1/2)∫e^(x^2)d(x^2)
=(1/2)e^(x^2)+C(C为常数)
代入上下限,可知
原积分=(e-1)/2