What is the integral from-1 to 3 of xe^{(2-x)} ?

The integral from-1 to 3 of xe^{(2-x)} is -4/e

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integral from-1 to 3 of xe^{(2-x)}

\int_{- 1}^{3} x e^{(2 - x)} d x

- \frac{4}{e}

Decimal

- 1.47151 \dots

Solution steps

\int_{- 1}^{3} x e^{2 - x} d x

Simplify

e^{2 - x} : e^{2} e^{- x}

= \int_{- 1}^{3} x e^{2} e^{- x} d x

Take the constant out:

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

= e^{2} \cdot \int_{- 1}^{3} x e^{- x} d x

Apply Integration By Parts

= e^{2} [- e^{- x} x - \int - e^{- x} d x]_{- 1}^{3}

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

= e^{2} [- e^{- x} x - e^{- x}]_{- 1}^{3}

Compute the boundaries:

- \frac{4}{e ^{3}}

= e^{2} (- \frac{4}{e ^{3}})

Simplify

= - \frac{4}{e}

What is the integral from-1 to 3 of xe^{(2-x)} ?
The integral from-1 to 3 of xe^{(2-x)} is -4/e