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

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

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

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

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

Solution steps

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

Compute the boundaries:

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

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

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

\int_{0}^{\frac{π}{2}} 4 x e^{x} sin (x) d x

\int_{1 - i}^{2 i} z^{2} - 6 - 4 i z d z

\int_{1}^{2} (24 x^{3} + \frac{6}{x ^{2}}) d x

\int_{0}^{10} t e^{- 0.2 t} d t

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