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人気のある微分積分 >

integral from 0 to pi/6 of (cos(3θ))^2

解

\int_{0}^{\frac{π}{6}} (cos (3 θ))^{2} d θ

解

\frac{π}{12}

+1

十進法表記

0.26179 \dots

解答ステップ

\int_{0}^{\frac{π}{6}} (cos (3 θ))^{2} d θ

簡素化

= \int_{0}^{\frac{π}{6}} cos^{2} (3 θ) d θ

三角関数の公式を使用して書き換える

= \int_{0}^{\frac{π}{6}} \frac{1}{2} (1 + cos (6 θ)) d θ

定数を除く:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{6}} 1 + cos (6 θ) d θ

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{0}^{\frac{π}{6}} 1 d θ + \int_{0}^{\frac{π}{6}} cos (6 θ) d θ)

\int_{0}^{\frac{π}{6}} 1 d θ = \frac{π}{6}

\int_{0}^{\frac{π}{6}} cos (6 θ) d θ = 0

= \frac{1}{2} (\frac{π}{6} + 0)

簡素化

\frac{1}{2} (\frac{π}{6} + 0) : \frac{π}{12}

= \frac{π}{12}

グラフ

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