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人気のある微分積分 >

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

解

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

解

3 - 6 ln (2)

+1

十進法表記

- 1.15888 \dots

解答ステップ

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

拡張

\frac{x - 3}{x} : 1 - \frac{3}{x}

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{4} 1 d x = 3

\int_{1}^{4} \frac{3}{x} d x = 6 ln (2)

= 3 - 6 ln (2)

グラフ

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