What is the integral from 6 to infinity of-xe^{-x} ?

The integral from 6 to infinity of-xe^{-x} is -7/(e^6)

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integral from 6 to infinity of-xe^{-x}

\int_{6}^{\infty} - x e^{- x} d x

- \frac{7}{e ^{6}}

Decimal

- 0.01735 \dots

Solution steps

\int_{6}^{\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_{6}^{\infty} - x e^{- x} d x = 0 - \frac{7}{e ^{6}}

= 0 - \frac{7}{e ^{6}}

Simplify

= - \frac{7}{e ^{6}}

What is the integral from 6 to infinity of-xe^{-x} ?
The integral from 6 to infinity of-xe^{-x} is -7/(e^6)