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人気のある微分積分 >

integral from 0 to 2 of (24)/(x^2+4)

解

\int_{0}^{2} \frac{24}{x ^{2} + 4} d x

解

3 π

+1

十進法表記

9.42477 \dots

解答ステップ

\int_{0}^{2} \frac{24}{x ^{2} + 4} d x

定数を除く:

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

= 24 \cdot \int_{0}^{2} \frac{1}{x ^{2} + 4} d x

置換積分法を適用する

= 24 \cdot \int_{0}^{1} \frac{1}{2 ( u ^{2} + 1 )} d u

定数を除く:

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

= 24 \cdot \frac{1}{2} \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

共通積分を使用する:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 24 \cdot \frac{1}{2} [arctan (u)]_{0}^{1}

簡素化

24 \cdot \frac{1}{2} [arctan (u)]_{0}^{1} : 12 [arctan (u)]_{0}^{1}

= 12 [arctan (u)]_{0}^{1}

限度を計算する:

\frac{π}{4}

= 12 \cdot \frac{π}{4}

簡素化

= 3 π

グラフ

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