What is the integral from 4x to x^2 of e^{-t^2} ?

The integral from 4x to x^2 of e^{-t^2} is (sqrt(pi))/2 \erf(x^2)-(sqrt(pi))/2 \erf(4x)

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integral from 4x to x^2 of e^{-t^2}

\int_{4 x}^{x^{2}} e^{- t^{2}} d t

\frac{π}{2} erf (x^{2}) - \frac{π}{2} erf (4 x)

Solution steps

\int_{4 x}^{x^{2}} 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)]_{4 x}^{x^{2}}

Compute the boundaries:

\frac{π}{2} erf (x^{2}) - \frac{π}{2} erf (4 x)

= \frac{π}{2} erf (x^{2}) - \frac{π}{2} erf (4 x)

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What is the integral from 4x to x^2 of e^{-t^2} ?
The integral from 4x to x^2 of e^{-t^2} is (sqrt(pi))/2 \erf(x^2)-(sqrt(pi))/2 \erf(4x)