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人気のある微分積分 >

integral from 0 to 2pi of 1/4 sin^2(x)

解

\int_{0}^{2 π} \frac{1}{4} sin^{2} (x) d x

解

\frac{π}{4}

+1

十進法表記

0.78539 \dots

解答ステップ

\int_{0}^{2 π} \frac{1}{4} sin^{2} (x) d x

定数を除く:

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

= \frac{1}{4} \cdot \int_{0}^{2 π} sin^{2} (x) d x

三角関数の公式を使用して書き換える

= \frac{1}{4} \cdot \int_{0}^{2 π} \frac{1 - cos ( 2 x )}{2} d x

定数を除く:

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

= \frac{1}{4} \cdot \frac{1}{2} \cdot \int_{0}^{2 π} 1 - cos (2 x) d x

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}{4} \cdot \frac{1}{2} (\int_{0}^{2 π} 1 d x - \int_{0}^{2 π} cos (2 x) d x)

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} cos (2 x) d x = 0

= \frac{1}{4} \cdot \frac{1}{2} (2 π - 0)

簡素化

\frac{1}{4} \cdot \frac{1}{2} (2 π - 0) : \frac{π}{4}

= \frac{π}{4}

グラフ

人気の例

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