What is the integral from 0 to y of xe^{-y} ?

The integral from 0 to y of xe^{-y} is (y^2e^{-y})/2

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integral from 0 to y of xe^{-y}

\int_{0}^{y} x e^{- y} d x

\frac{y ^{2} e ^{- y}}{2}

Solution steps

\int_{0}^{y} x e^{- y} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{- y} \cdot \int_{0}^{y} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{y}

= e^{- y} [\frac{x ^{2}}{2}]_{0}^{y}

Compute the boundaries:

\frac{y ^{2}}{2}

= e^{- y} \frac{y ^{2}}{2}

Simplify

= \frac{y ^{2} e ^{- y}}{2}

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What is the integral from 0 to y of xe^{-y} ?
The integral from 0 to y of xe^{-y} is (y^2e^{-y})/2