What is the integral from 0 to 1 of x^2e^{x-1} ?

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

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integral from 0 to 1 of x^2e^{x-1}

\int_{0}^{1} x^{2} e^{x - 1} d x

1 - \frac{2}{e}

Decimal

0.26424 \dots

Solution steps

\int_{0}^{1} x^{2} e^{x - 1} d x

Apply Integration By Parts

: [x^{2} e^{x - 1} - \int 2 x e^{x - 1} d x]_{0}^{1}

= [x^{2} e^{x - 1} - \int 2 x e^{x - 1} d x]_{0}^{1}

\int 2 x e^{x - 1} d x = 2 (e^{x - 1} x - e^{x - 1})

= [x^{2} e^{x - 1} - 2 (e^{x - 1} x - e^{x - 1})]_{0}^{1}

Compute the boundaries:

1 - \frac{2}{e}

= 1 - \frac{2}{e}

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\int_{3}^{5} - x^{2} + 8 x - 12 d x

\int_{2}^{8} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

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

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