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

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

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integral from-a to a of e^{x^2}

\int_{- a}^{a} e^{x^{2}} d x

\frac{π}{2} erfi (a) - \frac{π}{2} erfi (- a)

Solution steps

\int_{- a}^{a} e^{x^{2}} d x

Use the nonelementary integral:

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

= [\frac{π}{2} erfi (x)]_{- a}^{a}

Compute the boundaries:

\frac{π}{2} erfi (a) - \frac{π}{2} erfi (- a)

= \frac{π}{2} erfi (a) - \frac{π}{2} erfi (- a)

\int_{- 2}^{2} \frac{3}{4 + 3 t ^{2}} d t

\int_{- 1}^{4} x (x^{2} - 3)^{5} d x

\int_{1}^{4} x ln (2) + \frac{3}{2 x} d x

\int_{0}^{3} π (4 x^{2})^{2} d x

\int_{0}^{1} 4 - x^{2} d x

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