Question

Evaluate: `int_0^oo xe^-x.dx`

Answer 1

let u = x, u' = 1

let `int v'  = inte^-x, v=-e^-x`

`= [-xe^-x]_0^∞ + int_0^∞ e^-x . dx`

`= [-xe^-x]_0^∞ + [-e^-x]_0^∞`

`= [-xe^-x - e^-x]_0^∞`

`= \underset(x->∞)(lim) [-xe^-x - e^-x] - [-0e^-0 - e^-0]`

= [0 − 0] − [0 − 1]

= 1