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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{π}{2} erf (2 x)

Solution steps

\int_{0}^{2 x} 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}^{2 x}

Compute the boundaries:

\frac{π}{2} erf (2 x)

= \frac{π}{2} erf (2 x)

\int_{3}^{6} (3 x^{2} + x - 3) d x

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

\int_{0}^{x} \frac{t}{9 + t ^{2}} d t

\int_{1}^{2} x^{3} \cdot cos (x^{4}) d x

\int_{0}^{9} x - \frac{1}{2} x d x

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