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人気のある微分積分 >

integral from 2 to 3 of (18)/(6-x)

解

\int_{2}^{3} \frac{18}{6 - x} d x

解

18 (2 ln (2) - ln (3))

+1

十進法表記

5.17827 \dots

解答ステップ

\int_{2}^{3} \frac{18}{6 - x} d x

定数を除く:

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

= 18 \cdot \int_{2}^{3} \frac{1}{6 - x} d x

u置換積分法を適用する

= 18 \cdot \int_{4}^{3} - \frac{1}{u} d u

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

= 18 (- \int_{3}^{4} - \frac{1}{u} d u)

定数を除く:

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

= 18 (- (- \int_{3}^{4} \frac{1}{u} d u))

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 18 (- (- [ln ∣ u ∣]_{3}^{4}))

簡素化

= 18 [ln ∣ u ∣]_{3}^{4}

限度を計算する:

2 ln (2) - ln (3)

= 18 (2 ln (2) - ln (3))

グラフ

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