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人気のある微分積分 >

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

解

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

解

4

解答ステップ

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

簡素化

(x)^{2} : x

= \frac{1}{2} \cdot \int_{0}^{4} x d x

べき乗則を適用する

= \frac{1}{2} [\frac{x ^{2}}{2}]_{0}^{4}

限度を計算する:

8

= \frac{1}{2} \cdot 8

簡素化

= 4

グラフ

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