What is the integral from 0 to infinity of xe^{-kx} ?

The integral from 0 to infinity of xe^{-kx} is 1/(k^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to infinity of xe^{-kx}

\int_{0}^{\infty} x e^{- k x} d x

\frac{1}{k ^{2}}

Solution steps

\int_{0}^{\infty} x e^{- k x} d x

Compute the indefinite integral:

\int x e^{- k x} d x = \frac{1}{k ^{2}} (- k e^{- k x} x - e^{- k x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- k x} d x = 0 - (- \frac{1}{k ^{2}})

= 0 - (- \frac{1}{k ^{2}})

Simplify

= \frac{1}{k ^{2}}

\int_{1}^{3} x^{2} + 8 d x

\int_{x}^{1} x^{2} u^{2} + 1 d u

\int_{1}^{2} 2 x ln (3 x) d x

\int_{0}^{4} ∣ 5 - 3 x ∣ d x

\int_{0}^{4} (2 x - 1)^{2} d x

What is the integral from 0 to infinity of xe^{-kx} ?
The integral from 0 to infinity of xe^{-kx} is 1/(k^2)