What is the integral from 0 to infinity of x*e^{-2x} ?

The integral from 0 to infinity of x*e^{-2x} is 1/4

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 x*e^{-2x}

\int_{0}^{\infty} x \cdot e^{- 2 x} d x

\frac{1}{4}

Decimal

0.25

Solution steps

\int_{0}^{\infty} x e^{- 2 x} d x

Compute the indefinite integral:

\int x e^{- 2 x} d x = \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- 2 x} d x = 0 - (- \frac{1}{4})

= 0 - (- \frac{1}{4})

Simplify

= \frac{1}{4}

\frac{d y}{d x} = y \cdot tan (x) + 1

\frac{d ^{2}}{d x ^{2}} (2^{x^{2} + 1})

\frac{d y}{d x} = e^{5 y}

\frac{d}{d x} (e^{- 2 x} sin (x))

x \to - 1 lim (\frac{∣ x ∣}{x})

What is the integral from 0 to infinity of x*e^{-2x} ?
The integral from 0 to infinity of x*e^{-2x} is 1/4