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人気のある微分積分 >

integral from 3 to 9 of |1-9/x |

解

\int_{3}^{9} 1 - \frac{9}{x} d x

解

- 6 + 9 ln (3)

+1

十進法表記

3.88751 \dots

解答ステップ

\int_{3}^{9} 1 - \frac{9}{x} d x

絶対数を排除する

= \int_{3}^{9} - 1 + \frac{9}{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_{3}^{9} 1 d x + \int_{3}^{9} \frac{9}{x} d x

\int_{3}^{9} 1 d x = 6

\int_{3}^{9} \frac{9}{x} d x = 9 ln (3)

= - 6 + 9 ln (3)

グラフ

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