integral from 0 to 4 of x^3-10x^2+24x

解

\int_{0}^{4} x^{3} - 10 x^{2} + 24 x d x

\frac{128}{3}

十進法表記

42.66666 \dots

解答ステップ

\int_{0}^{4} x^{3} - 10 x^{2} + 24 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} x^{3} d x - \int_{0}^{4} 10 x^{2} d x + \int_{0}^{4} 24 x d x

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

\int_{0}^{4} 10 x^{2} d x = \frac{640}{3}

\int_{0}^{4} 24 x d x = 192

= 64 - \frac{640}{3} + 192

簡素化

64 - \frac{640}{3} + 192 : \frac{128}{3}

= \frac{128}{3}