Question

求广义积分∫﹙0﹣﹢∞﹚te的-t／2次方dt

Answer 1

∫﹙0-->﹢∞﹚te^(-t/2)dt

=-2∫﹙0-->﹢∞﹚te^(-t/2)d(-t/2)

=-2∫﹙0-->﹢∞﹚td(e^(-t/2))

=-2te^(-t/2)+2∫﹙0-->﹢∞﹚e^(-t/2)dt

=-2te^(-t/2)-4e^(-t/2) ﹙0-->﹢∞﹚

=4