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人気のある微分積分 >

integral from 0 to 6 of (300)/(3Q+2)

解

\int_{0}^{6} \frac{300}{3 Q + 2} d Q

解

100 ln (10)

+1

十進法表記

230.25850 \dots

解答ステップ

\int_{0}^{6} \frac{300}{3 Q + 2} d Q

定数を除く:

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

= 300 \cdot \int_{0}^{6} \frac{1}{3 Q + 2} d Q

u置換積分法を適用する

= 300 \cdot \int_{2}^{20} \frac{1}{3 u} d u

定数を除く:

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

= 300 \cdot \frac{1}{3} \cdot \int_{2}^{20} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 300 \cdot \frac{1}{3} [ln ∣ u ∣]_{2}^{20}

簡素化

300 \cdot \frac{1}{3} [ln ∣ u ∣]_{2}^{20} : 100 [ln ∣ u ∣]_{2}^{20}

= 100 [ln ∣ u ∣]_{2}^{20}

限度を計算する:

ln (20) - ln (2)

= 100 (ln (20) - ln (2))

簡素化

= 100 ln (10)

グラフ

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