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人気のある微分積分 >

integral from 1 to 4 of pi(sqrt(x-1))^2

解

\int_{1}^{4} π (x - 1)^{2} d x

解

π \frac{9}{2}

+1

十進法表記

14.13716 \dots

解答ステップ

\int_{1}^{4} π (x - 1)^{2} d x

定数を除く:

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

= π \cdot \int_{1}^{4} (x - 1)^{2} d x

簡素化

(x - 1)^{2} : x - 1

= π \cdot \int_{1}^{4} x - 1 d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{1}^{4} x d x - \int_{1}^{4} 1 d x)

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} 1 d x = 3

= π (\frac{15}{2} - 3)

結合

\frac{15}{2} - 3 : \frac{9}{2}

= π \frac{9}{2}

グラフ

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