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

解答

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

\frac{π}{2} erf (\frac{y}{4})

求解步骤

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

这是非初等函数积分:

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

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

带入上下限计算后得:

\frac{π}{2} erf (\frac{y}{4})

= \frac{π}{2} erf (\frac{y}{4})

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