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

解答

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

\frac{π}{2} erf (\frac{x}{4})

求解步骤

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

这是非初等函数积分:

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

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

带入上下限计算后得:

\frac{π}{2} erf (\frac{x}{4})

= \frac{π}{2} erf (\frac{x}{4})

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