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人気のある微分積分 >

integral from 0 to 2 of 4sec((pix)/6)

解

\int_{0}^{2} 4 sec (\frac{π x}{6}) d x

解

\frac{24}{π} ln (2 + 3)

+1

十進法表記

10.06081 \dots

解答ステップ

\int_{0}^{2} 4 sec (\frac{π x}{6}) d x

定数を除く:

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

= 4 \cdot \int_{0}^{2} sec (\frac{π x}{6}) d x

u置換積分法を適用する

= 4 \cdot \int_{0}^{\frac{π}{3}} sec (u) \frac{6}{π} d u

定数を除く:

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

= 4 \cdot \frac{6}{π} \cdot \int_{0}^{\frac{π}{3}} sec (u) d u

共通積分を使用する:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= 4 \cdot \frac{6}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

簡素化

4 \cdot \frac{6}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}} : \frac{24}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

= \frac{24}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

限度を計算する:

ln (2 + 3)

= \frac{24}{π} ln (2 + 3)

グラフ

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