What is the integral from 0 to x/4 of e^{-x^2} ?

The integral from 0 to x/4 of e^{-x^2} is (sqrt(pi))/2 \erf(x/4)

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integral from 0 to x/4 of e^{-x^2}

\int_{0}^{\frac{x}{4}} e^{- x^{2}} d x

\frac{π}{2} erf (\frac{x}{4})

Solution steps

\int_{0}^{\frac{x}{4}} e^{- x^{2}} d x

Use the nonelementary integral:

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

= [\frac{π}{2} erf (x)]_{0}^{\frac{x}{4}}

Compute the boundaries:

\frac{π}{2} erf (\frac{x}{4})

= \frac{π}{2} erf (\frac{x}{4})

\int_{1}^{3} \frac{1}{x 4 + x ^{2}} d x

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

\int_{- 1}^{1} (2 - x^{2} - x^{2}) d x

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

\int_{1}^{4} 5 x^{4} d x

What is the integral from 0 to x/4 of e^{-x^2} ?
The integral from 0 to x/4 of e^{-x^2} is (sqrt(pi))/2 \erf(x/4)