Question

∫（正无穷~0）kxe^(-x^2)dx=1 求k,用凑微分还是分部积分法?

Answer 1

当然是用凑微分了.此题不能用分部积分法.

∫（正无穷~0）kxe^(-x^2)dx=(-k/2)∫（正无穷~0）e^(-x^2)d(-x^2)

=(-k/2)e^(-x^2)(正无穷~0)=(-k/2)=1,k=-2.