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

The integral from 0 to 1 of x^2e^{x^2} is e/2-(sqrt(pi))/4 \erfi(1)

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

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

\frac{e}{2} - \frac{π}{4} erfi (1)

Solution steps

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

Simplify

x^{2} : xx

= \int_{0}^{1} xx e^{x^{2}} d x

Apply Integration By Parts

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

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

\int \frac{1}{2} e^{x^{2}} d x = \frac{π}{4} erfi (x)

= [\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)]_{0}^{1}

Compute the boundaries:

\frac{e}{2} - \frac{π}{4} erfi (1)

= \frac{e}{2} - \frac{π}{4} erfi (1)

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What is the integral from 0 to 1 of x^2e^{x^2} ?
The integral from 0 to 1 of x^2e^{x^2} is e/2-(sqrt(pi))/4 \erfi(1)