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人気のある微分積分 >

integral from 0 to 2 of x3^{-x^2}

解

\int_{0}^{2} x 3^{- x^{2}} d x

解

\frac{40}{81 ln ( 3 )}

+1

十進法表記

0.44950 \dots

解答ステップ

\int_{0}^{2} x \cdot 3^{- x^{2}} d x

u置換積分法を適用する

= \int_{1}^{\frac{1}{81}} - \frac{1}{2 ln ( 3 )} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{\frac{1}{81}}^{1} - \frac{1}{2 ln ( 3 )} d u

定数の積分:

\int a d x = a x

= - [(- \frac{1}{2 ln ( 3 )}) u]_{\frac{1}{81}}^{1}

簡素化

= - [- \frac{1}{2 ln ( 3 )} u]_{\frac{1}{81}}^{1}

限度を計算する:

- \frac{40}{81 ln ( 3 )}

= - (- \frac{40}{81 ln ( 3 )})

簡素化

= \frac{40}{81 ln ( 3 )}

グラフ

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