What is the integral from 0 to t/3 of e^{t^2} ?

The integral from 0 to t/3 of e^{t^2} is (sqrt(pi))/2 \erfi(t/3)

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integral from 0 to t/3 of e^{t^2}

\int_{0}^{\frac{t}{3}} e^{t^{2}} d t

\frac{π}{2} erfi (\frac{t}{3})

Solution steps

\int_{0}^{\frac{t}{3}} 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)]_{0}^{\frac{t}{3}}

Compute the boundaries:

\frac{π}{2} erfi (\frac{t}{3})

= \frac{π}{2} erfi (\frac{t}{3})

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What is the integral from 0 to t/3 of e^{t^2} ?
The integral from 0 to t/3 of e^{t^2} is (sqrt(pi))/2 \erfi(t/3)