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人気のある微分積分 >

integral from 0 to pi/(30) of 20cos(5x)

解

\int_{0}^{\frac{π}{30}} 20 cos (5 x) d x

解

2

解答ステップ

\int_{0}^{\frac{π}{30}} 20 cos (5 x) d x

定数を除く:

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

= 20 \cdot \int_{0}^{\frac{π}{30}} cos (5 x) d x

u置換積分法を適用する

= 20 \cdot \int_{0}^{\frac{π}{6}} cos (u) \frac{1}{5} d u

定数を除く:

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

= 20 \cdot \frac{1}{5} \cdot \int_{0}^{\frac{π}{6}} cos (u) d u

共通積分を使用する:

\int cos (u) d u = sin (u)

= 20 \cdot \frac{1}{5} [sin (u)]_{0}^{\frac{π}{6}}

簡素化

20 \cdot \frac{1}{5} [sin (u)]_{0}^{\frac{π}{6}} : 4 [sin (u)]_{0}^{\frac{π}{6}}

= 4 [sin (u)]_{0}^{\frac{π}{6}}

限度を計算する:

\frac{1}{2}

= 4 \cdot \frac{1}{2}

簡素化

= 2

グラフ

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