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人気のある微分積分 >

integral from 0 to pi/2 of cos(1/2 x)

解

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

解

2

+1

十進法表記

1.41421 \dots

解答ステップ

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

u置換積分法を適用する

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

定数を除く:

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

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

共通積分を使用する:

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

= 2 [sin (u)]_{0}^{\frac{π}{4}}

限度を計算する:

\frac{1}{2}

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

簡素化

= 2

グラフ

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