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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to tan(x) of e^{-t^2}

\int_{0}^{t a n (x)} e^{- t^{2}} d t

\frac{π}{2} erf (tan (x))

Solution steps

\int_{0}^{t a n (x)} e^{- t^{2}} d t

Use the nonelementary integral:

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

= [\frac{π}{2} erf (t)]_{0}^{t a n (x)}

Compute the boundaries:

\frac{π}{2} erf (tan (x))

= \frac{π}{2} erf (tan (x))

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