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人気のある微分積分 >

integral from 0 to 2 of x/(1+10x^2)

解

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

解

\frac{1}{20} ln (41)

+1

十進法表記

0.18567 \dots

解答ステップ

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

u置換積分法を適用する

= \int_{1}^{41} \frac{1}{20 u} d u

定数を除く:

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

= \frac{1}{20} \cdot \int_{1}^{41} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{20} [ln ∣ u ∣]_{1}^{41}

限度を計算する:

ln (41)

= \frac{1}{20} ln (41)

グラフ

人気の例

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