What is the integral from cos(x) to 1 of e^{-t^2} ?

The integral from cos(x) to 1 of e^{-t^2} is 0.74682…-0.88622…\erf(cos(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from cos(x) to 1 of e^{-t^2}

\int_{c o s (x)}^{1} e^{- t^{2}} d t

0.74682 \dots - 0.88622 \dots erf (cos (x))

Solution steps

\int_{c o s (x)}^{1} 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)]_{c o s (x)}^{1}

Compute the boundaries:

0.74682 \dots - 0.88622 \dots erf (cos (x))

= 0.74682 \dots - 0.88622 \dots erf (cos (x))

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

\int_{1}^{e^{2}} \frac{ln ( x )}{x} d x

\int_{0}^{\frac{π}{4}} x sin (x) d x

\int_{0}^{2 π} x cos (x) d x

\int_{- 2}^{1} (3 + y^{2}) - (2 - y^{2}) d y

What is the integral from cos(x) to 1 of e^{-t^2} ?
The integral from cos(x) to 1 of e^{-t^2} is 0.74682…-0.88622…\erf(cos(x))