What is the integral from 0 to 50 of xe^{-x/(14)} ?

The integral from 0 to 50 of xe^{-x/(14)} is -(896)/(e^{25/7)}+196

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integral from 0 to 50 of xe^{-x/(14)}

\int_{0}^{50} x e^{- \frac{x}{14}} d x

- \frac{896}{e ^{\frac{25}{7}}} + 196

Decimal

170.80836 \dots

Solution steps

\int_{0}^{50} x e^{- \frac{x}{14}} d x

Apply Integration By Parts

= [- 14 e^{- \frac{x}{14}} x - \int - 14 e^{- \frac{x}{14}} d x]_{0}^{50}

\int - 14 e^{- \frac{x}{14}} d x = 196 e^{- \frac{x}{14}}

= [- 14 e^{- \frac{x}{14}} x - 196 e^{- \frac{x}{14}}]_{0}^{50}

Compute the boundaries:

- \frac{896}{e ^{\frac{25}{7}}} + 196

= - \frac{896}{e ^{\frac{25}{7}}} + 196

What is the integral from 0 to 50 of xe^{-x/(14)} ?
The integral from 0 to 50 of xe^{-x/(14)} is -(896)/(e^{25/7)}+196