What is the integral from 0 to 100 of xe^{-x/(12)} ?

The integral from 0 to 100 of xe^{-x/(12)} is -(1344)/(e^{25/3)}+144

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integral from 0 to 100 of xe^{-x/(12)}

\int_{0}^{100} x e^{- \frac{x}{12}} d x

- \frac{1344}{e ^{\frac{25}{3}}} + 144

Decimal

143.67694 \dots

Solution steps

\int_{0}^{100} x e^{- \frac{x}{12}} d x

Apply Integration By Parts

= [- 12 e^{- \frac{x}{12}} x - \int - 12 e^{- \frac{x}{12}} d x]_{0}^{100}

\int - 12 e^{- \frac{x}{12}} d x = 144 e^{- \frac{x}{12}}

= [- 12 e^{- \frac{x}{12}} x - 144 e^{- \frac{x}{12}}]_{0}^{100}

Compute the boundaries:

- \frac{1344}{e ^{\frac{25}{3}}} + 144

= - \frac{1344}{e ^{\frac{25}{3}}} + 144

What is the integral from 0 to 100 of xe^{-x/(12)} ?
The integral from 0 to 100 of xe^{-x/(12)} is -(1344)/(e^{25/3)}+144