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人気のある微分積分 >

integral from 2 to 8 of-6/x

解

\int_{2}^{8} - \frac{6}{x} d x

解

- 12 ln (2)

+1

十進法表記

- 8.31776 \dots

解答ステップ

\int_{2}^{8} - \frac{6}{x} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 6 \cdot \int_{2}^{8} \frac{1}{x} d x

共通積分を使用する:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - 6 [ln ∣ x ∣]_{2}^{8}

限度を計算する:

2 ln (2)

= - 6 \cdot 2 ln (2)

簡素化

= - 12 ln (2)

グラフ

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