integral from-5 to 6 of (36-x^2)-(6-x)

解

\int_{- 5}^{6} (36 - x^{2}) - (6 - x) d x

\frac{1331}{6}

十進法表記

221.83333 \dots

解答ステップ

\int_{- 5}^{6} 36 - x^{2} - (6 - x) d x

簡素化

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

\int_{- 5}^{6} x^{2} d x = \frac{341}{3}

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

\int_{- 5}^{6} 30 d x = 330

= - \frac{341}{3} + \frac{11}{2} + 330

簡素化

- \frac{341}{3} + \frac{11}{2} + 330 : \frac{1331}{6}

= \frac{1331}{6}