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人気のある微分積分 >

integral from 0 to 1 of (12x)/(x^2+7)

解

\int_{0}^{1} \frac{12 x}{x ^{2} + 7} d x

解

6 (3 ln (2) - ln (7))

+1

十進法表記

0.80118 \dots

解答ステップ

\int_{0}^{1} \frac{12 x}{x ^{2} + 7} d x

定数を除く:

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

= 12 \cdot \int_{0}^{1} \frac{x}{x ^{2} + 7} d x

u置換積分法を適用する

= 12 \cdot \int_{7}^{8} \frac{1}{2 u} d u

定数を除く:

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

= 12 \cdot \frac{1}{2} \cdot \int_{7}^{8} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 12 \cdot \frac{1}{2} [ln ∣ u ∣]_{7}^{8}

簡素化

12 \cdot \frac{1}{2} [ln ∣ u ∣]_{7}^{8} : 6 [ln ∣ u ∣]_{7}^{8}

= 6 [ln ∣ u ∣]_{7}^{8}

限度を計算する:

3 ln (2) - ln (7)

= 6 (3 ln (2) - ln (7))

グラフ

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