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人気のある微分積分 >

integral from 0 to pi of sqrt(cos^2(x))

解

\int_{0}^{π} cos^{2} (x) d x

解

2

解答ステップ

\int_{0}^{π} cos^{2} (x) d x

指数の規則を適用する:

a^{2} = ∣ a ∣

= \int_{0}^{π} ∣ cos (x) ∣ d x

絶対数を排除する

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

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

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

= 1 + 1

簡素化

= 2

グラフ

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