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

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

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

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

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

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} erfi (t)]_{- 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^{t^2} ?
The integral from-1 to x of e^{t^2} is (sqrt(pi))/2 \erfi(x)-(sqrt(pi))/2 \erfi(-1)