integral from 0 to 5 of pi(25-y^2)

解

\int_{0}^{5} π (25 - y^{2}) d y

π \frac{250}{3}

十進法表記

261.79938 \dots

解答ステップ

\int_{0}^{5} π (25 - y^{2}) d y

定数を除く:

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

= π \cdot \int_{0}^{5} 25 - y^{2} d y

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_{0}^{5} 25 d y - \int_{0}^{5} y^{2} d y)

\int_{0}^{5} 25 d y = 125

\int_{0}^{5} y^{2} d y = \frac{125}{3}

= π (125 - \frac{125}{3})

結合

125 - \frac{125}{3} : \frac{250}{3}

= π \frac{250}{3}