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人気のある微分積分 >

integral from 0 to 6 of 6sin(0.3t)

解

\int_{0}^{6} 6 sin (0.3 t) d t

解

24.54404 \dots

解答ステップ

\int_{0}^{6} 6 sin (0.3 t) d t

定数を除く:

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

= 6 \cdot \int_{0}^{6} sin (0.3 t) d t

u置換積分法を適用する

= 6 \cdot \int_{0}^{1.8} sin (u) \frac{1}{0.3} d u

定数を除く:

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

= 6 \cdot \frac{1}{0.3} \cdot \int_{0}^{1.8} sin (u) d u

簡素化

= 6 \cdot 3.33333 \dots \cdot \int_{0}^{1.8} sin (u) d u

共通積分を使用する:

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

= 6 \cdot 3.33333 \dots [- cos (u)]_{0}^{1.8}

簡素化

= 20 [- cos (u)]_{0}^{1.8}

限度を計算する:

1.22720 \dots

= 20 \cdot 1.22720 \dots

簡素化

= 24.54404 \dots

グラフ

人気の例

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