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人気のある微分積分 >

integral from 3x to x^5 of e^{-t^2}

解

\int_{3 x}^{x^{5}} e^{- t^{2}} d t

解

\frac{π}{2} erf (x^{5}) - \frac{π}{2} erf (3 x)

解答ステップ

\int_{3 x}^{x^{5}} e^{- t^{2}} d t

非初等積分を使用する:

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

= [\frac{π}{2} erf (t)]_{3 x}^{x^{5}}

限度を計算する:

\frac{π}{2} erf (x^{5}) - \frac{π}{2} erf (3 x)

= \frac{π}{2} erf (x^{5}) - \frac{π}{2} erf (3 x)

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