What is the integral from 0 to 1 of xe^{x-1} ?

The integral from 0 to 1 of xe^{x-1} is 1/e

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integral from 0 to 1 of xe^{x-1}

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

\frac{1}{e}

Decimal

0.36787 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int e^{x - 1} d x = e^{x - 1}

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

Compute the boundaries:

\frac{1}{e}

= \frac{1}{e}

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What is the integral from 0 to 1 of xe^{x-1} ?
The integral from 0 to 1 of xe^{x-1} is 1/e