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

The integral from 0 to infinity of x^2e^{-x/2} is 16

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^2e^{-x/2}

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

16

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} x^{2} e^{- \frac{x}{2}} d x = 0 - (- 16)

= 0 - (- 16)

Simplify

= 16

x \to 0 + lim (x e^{s i n (\frac{π}{x})})

sin (x) π

\int \frac{6 ln ^{2} ( x )}{x} d x

\int \frac{- 4 x}{( 1 - 2 x ^{2} ) ^{2}} d x

ln (\frac{1 + x}{1 - x}), 0

What is the integral from 0 to infinity of x^2e^{-x/2} ?
The integral from 0 to infinity of x^2e^{-x/2} is 16