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人気のある微分積分 >

integral from 0 to 3 of 5/(x^2+1)

解

\int_{0}^{3} \frac{5}{x ^{2} + 1} d x

解

5 arctan (3)

+1

十進法表記

6.24522 \dots

解答ステップ

\int_{0}^{3} \frac{5}{x ^{2} + 1} d x

定数を除く:

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

= 5 \cdot \int_{0}^{3} \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)

= 5 [arctan (x)]_{0}^{3}

限度を計算する:

arctan (3)

= 5 arctan (3)

グラフ

人気の例

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