integral from 2 to 5 of x^3-3x^2+x

解

\int_{2}^{5} x^{3} - 3 x^{2} + x d x

\frac{183}{4}

十進法表記

45.75

解答ステップ

\int_{2}^{5} x^{3} - 3 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_{2}^{5} x^{3} d x - \int_{2}^{5} 3 x^{2} d x + \int_{2}^{5} x d x

\int_{2}^{5} x^{3} d x = \frac{609}{4}

\int_{2}^{5} 3 x^{2} d x = 117

\int_{2}^{5} x d x = \frac{21}{2}

= \frac{609}{4} - 117 + \frac{21}{2}

簡素化

\frac{609}{4} - 117 + \frac{21}{2} : \frac{183}{4}

= \frac{183}{4}