What is the integral from 5x to x^3 of e^{-t^2} ?

The integral from 5x to x^3 of e^{-t^2} is (sqrt(pi))/2 \erf(x^3)-(sqrt(pi))/2 \erf(5x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 5x to x^3 of e^{-t^2}

\int_{5 x}^{x^{3}} e^{- t^{2}} d t

\frac{π}{2} erf (x^{3}) - \frac{π}{2} erf (5 x)

Solution steps

\int_{5 x}^{x^{3}} 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)]_{5 x}^{x^{3}}

Compute the boundaries:

\frac{π}{2} erf (x^{3}) - \frac{π}{2} erf (5 x)

= \frac{π}{2} erf (x^{3}) - \frac{π}{2} erf (5 x)

\int_{- 4}^{1} x^{3} + x^{2} - 10 x + 8 d x

\int_{- 1}^{27} x^{- \frac{1}{3}} d x

\int_{0}^{6} - 3 x^{2} - 9 x + 162 d x

\int_{- 1}^{5} (3 x^{2} + 4 x) d x

\int_{2}^{3} \frac{1}{ln ( x )} d x

What is the integral from 5x to x^3 of e^{-t^2} ?
The integral from 5x to x^3 of e^{-t^2} is (sqrt(pi))/2 \erf(x^3)-(sqrt(pi))/2 \erf(5x)