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

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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

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