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人気のある微分積分 >

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

解

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

解

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

解答ステップ

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

限度を計算する:

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

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

人気の例

integral from 1/e to e of 1/(xln(x))

\int_{\frac{1}{e}}^{e} \frac{1}{x ln ( x )} d x

integral from 0 to 1 of 20x^3(1-x)

\int_{0}^{1} 20 x^{3} (1 - x) d x

integral from 1/3 to 3 of 4-4/(x^2)

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

integral from 1 to 4 of (7/x-e^{-x})

\int_{1}^{4} (\frac{7}{x} - e^{- x}) d x

integral from 0 to 3 of (3x^2-4x^2+1)

\int_{0}^{3} (3 x^{2} - 4 x^{2} + 1) d x