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

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

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

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

\frac{π}{2 2} erfi (2)

Solution steps

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

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

Apply u-substitution

: \int_{0}^{2} e^{u^{2}} \frac{1}{2} d u

= \int_{0}^{2} e^{u^{2}} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2} e^{u^{2}} d u

Use the nonelementary integral:

\int e^{u^{2}} d u = \frac{π}{2} erfi (u)

= \frac{1}{2} [\frac{π}{2} erfi (u)]_{0}^{2}

Compute the boundaries:

\frac{π}{2} erfi (2)

= \frac{1}{2} \cdot \frac{π}{2} erfi (2)

Simplify

= \frac{π}{2 2} erfi (2)

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