integral from 5 to 6 of-x^3+11x^2-30x

解

\int_{5}^{6} - x^{3} + 11 x^{2} - 30 x d x

\frac{11}{12}

十進法表記

0.91666 \dots

解答ステップ

\int_{5}^{6} - x^{3} + 11 x^{2} - 30 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_{5}^{6} x^{3} d x + \int_{5}^{6} 11 x^{2} d x - \int_{5}^{6} 30 x d x

\int_{5}^{6} x^{3} d x = \frac{671}{4}

\int_{5}^{6} 11 x^{2} d x = \frac{1001}{3}

\int_{5}^{6} 30 x d x = 165

= - \frac{671}{4} + \frac{1001}{3} - 165

簡素化

- \frac{671}{4} + \frac{1001}{3} - 165 : \frac{11}{12}

= \frac{11}{12}