What is the integral from 0 to infinity of xe^{-x/4} ?

The integral from 0 to infinity of xe^{-x/4} is 16

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integral from 0 to infinity of xe^{-x/4}

\int_{0}^{\infty} x e^{- \frac{x}{4}} d x

16

Solution steps

\int_{0}^{\infty} x e^{- \frac{x}{4}} d x

Compute the indefinite integral:

\int x e^{- \frac{x}{4}} d x = - 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}} + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- \frac{x}{4}} d x = 0 - (- 16)

= 0 - (- 16)

Simplify

= 16

y = x^{2}, (- 0.7, 0.49)

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What is the integral from 0 to infinity of xe^{-x/4} ?
The integral from 0 to infinity of xe^{-x/4} is 16