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

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

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

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

\frac{π}{2} erfi (x) - \frac{π}{2} erfi (- 1)

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} erfi (y)]_{- 1}^{x}

Compute the boundaries:

\frac{π}{2} erfi (x) - \frac{π}{2} erfi (- 1)

= \frac{π}{2} erfi (x) - \frac{π}{2} erfi (- 1)

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