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