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

The integral from 0 to a of e^{-x^2} is (sqrt(pi))/2 \erf(a)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to a of e^{-x^2}

\int_{0}^{a} e^{- x^{2}} d x

\frac{π}{2} erf (a)

Solution steps

\int_{0}^{a} e^{- x^{2}} d x

Use the nonelementary integral:

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

= [\frac{π}{2} erf (x)]_{0}^{a}

Compute the boundaries:

\frac{π}{2} erf (a)

= \frac{π}{2} erf (a)

\int_{0}^{x} (x - 2 y) d y

\int_{1}^{7} \frac{6}{x} d x

\int_{0}^{1} x^{3} cos (x) d x

\int_{0}^{π} - cos (2 y) + cos (y) d y

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos^{8} (x) d x

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