Question

∫xe^xdx(积分限0到1)

Answer 1

分虚凳型部积分：
∫ x e^x dx = ∫ x d(e^x)
= x e^x - ∫ e^x dx = x e^x - e^x + C
∴差猜 I = (x-1) e^x |[0,1] Newton-Leibniz公式粗塌
= 1