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人気のある微分積分 >

integral from-1 to 1 of (4/(x^2+1))

解

\int_{- 1}^{1} (\frac{4}{x ^{2} + 1}) d x

解

2 π

+1

十進法表記

6.28318 \dots

解答ステップ

\int_{- 1}^{1} \frac{4}{x ^{2} + 1} d x

定数を除く:

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

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

共通積分を使用する:

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

= 4 [arctan (x)]_{- 1}^{1}

限度を計算する:

\frac{π}{2}

= 4 \cdot \frac{π}{2}

簡素化

= 2 π

グラフ

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