What is the integral from 4 to 5 of xe^{-x} ?

The integral from 4 to 5 of xe^{-x} is -6/(e^5)+5/(e^4)

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integral from 4 to 5 of xe^{-x}

\int_{4}^{5} x e^{- x} d x

- \frac{6}{e ^{5}} + \frac{5}{e ^{4}}

Decimal

0.05115 \dots

Solution steps

\int_{4}^{5} x e^{- x} d x

Apply Integration By Parts

= [- e^{- x} x - \int - e^{- x} d x]_{4}^{5}

\int - e^{- x} d x = e^{- x}

= [- e^{- x} x - e^{- x}]_{4}^{5}

Compute the boundaries:

- \frac{6}{e ^{5}} + \frac{5}{e ^{4}}

= - \frac{6}{e ^{5}} + \frac{5}{e ^{4}}

What is the integral from 4 to 5 of xe^{-x} ?
The integral from 4 to 5 of xe^{-x} is -6/(e^5)+5/(e^4)