What is the integral from 12 to infinity of xe^{-x} ?

The integral from 12 to infinity of xe^{-x} is (13)/(e^{12)}

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integral from 12 to infinity of xe^{-x}

\int_{12}^{\infty} x e^{- x} d x

\frac{13}{e ^{12}}

Decimal

0.00007 \dots

Solution steps

\int_{12}^{\infty} x e^{- x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{12}^{\infty} x e^{- x} d x = 0 - (- \frac{13}{e ^{12}})

= 0 - (- \frac{13}{e ^{12}})

Simplify

= \frac{13}{e ^{12}}

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What is the integral from 12 to infinity of xe^{-x} ?
The integral from 12 to infinity of xe^{-x} is (13)/(e^{12)}