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

解

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

\frac{500}{3}

十進法表記

166.66666 \dots

解答ステップ

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

簡素化

(25 - x^{2})^{2} : 25 - x^{2}

= \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

= \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}

= 250 - \frac{250}{3}

簡素化

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

= \frac{500}{3}