What is the integral from 0 to-1 of x*e^x ?

The integral from 0 to-1 of x*e^x is 1-2/e

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integral from 0 to-1 of x*e^x

\int_{0}^{- 1} x \cdot e^{x} d x

1 - \frac{2}{e}

Solution steps

\int_{0}^{- 1} x e^{x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{0} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{- 1}^{0}

= - [e^{x} x - \int e^{x} d x]_{- 1}^{0}

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

= - [e^{x} x - e^{x}]_{- 1}^{0}

Compute the boundaries:

- 1 + \frac{2}{e}

= - (- 1 + \frac{2}{e})

Simplify

= 1 - \frac{2}{e}

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What is the integral from 0 to-1 of x*e^x ?
The integral from 0 to-1 of x*e^x is 1-2/e