integral from 0 to 4 of (4x^2+sqrt(x))

解

\int_{0}^{4} (4 x^{2} + x) d x

\frac{272}{3}

十進法表記

90.66666 \dots

解答ステップ

\int_{0}^{4} 4 x^{2} + x 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} 4 x^{2} d x + \int_{0}^{4} x d x

\int_{0}^{4} 4 x^{2} d x = \frac{256}{3}

\int_{0}^{4} x d x = \frac{16}{3}

= \frac{256}{3} + \frac{16}{3}

簡素化

\frac{256}{3} + \frac{16}{3} : \frac{272}{3}

= \frac{272}{3}