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人気のある微分積分 >

integral from 5 to 11 of (16)/(x-1)

解

\int_{5}^{11} \frac{16}{x - 1} d x

解

16 ln (\frac{5}{2})

+1

十進法表記

14.66065 \dots

解答ステップ

\int_{5}^{11} \frac{16}{x - 1} d x

定数を除く:

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

= 16 \cdot \int_{5}^{11} \frac{1}{x - 1} d x

u置換積分法を適用する

= 16 \cdot \int_{4}^{10} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 16 [ln ∣ u ∣]_{4}^{10}

限度を計算する:

ln (10) - 2 ln (2)

= 16 (ln (10) - 2 ln (2))

簡素化

= 16 ln (\frac{5}{2})

グラフ

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