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人気のある微分積分 >

integral from 0 to 4 of 1/(36x^2+25)

解

\int_{0}^{4} \frac{1}{36 x ^{2} + 25} d x

解

\frac{1}{30} arctan (\frac{24}{5})

+1

十進法表記

0.04551 \dots

解答ステップ

\int_{0}^{4} \frac{1}{36 x ^{2} + 25} d x

置換積分法を適用する

= \int_{0}^{\frac{24}{5}} \frac{1}{30 ( u ^{2} + 1 )} d u

定数を除く:

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

= \frac{1}{30} \cdot \int_{0}^{\frac{24}{5}} \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)

= \frac{1}{30} [arctan (u)]_{0}^{\frac{24}{5}}

限度を計算する:

arctan (\frac{24}{5})

= \frac{1}{30} arctan (\frac{24}{5})

グラフ

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