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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{π}{2} erfi (x^{2})

Solution steps

\int_{0}^{x^{2}} 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)]_{0}^{x^{2}}

Compute the boundaries:

\frac{π}{2} erfi (x^{2})

= \frac{π}{2} erfi (x^{2})

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