integral from 0 to 4 of 25-x^2

解

\int_{0}^{4} 25 - x^{2} d x

\frac{236}{3}

十進法表記

78.66666 \dots

解答ステップ

\int_{0}^{4} 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_{0}^{4} 25 d x - \int_{0}^{4} x^{2} d x

\int_{0}^{4} 25 d x = 100

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= 100 - \frac{64}{3}

簡素化

100 - \frac{64}{3} : \frac{236}{3}

= \frac{236}{3}