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

解

\int_{- 5}^{5} π (25 - x^{2}) d x

π \frac{500}{3}

十進法表記

523.59877 \dots

解答ステップ

\int_{- 5}^{5} π (25 - x^{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_{- 5}^{5} 25 - x^{2} 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_{- 5}^{5} 25 d x - \int_{- 5}^{5} x^{2} d x)

\int_{- 5}^{5} 25 d x = 250

\int_{- 5}^{5} x^{2} d x = \frac{250}{3}

= π (250 - \frac{250}{3})

結合

250 - \frac{250}{3} : \frac{500}{3}

= π \frac{500}{3}