integral from-1 to 9 of (9-x^2)-(-8x)

解

\int_{- 1}^{9} (9 - x^{2}) - (- 8 x) d x

\frac{500}{3}

十進法表記

166.66666 \dots

解答ステップ

\int_{- 1}^{9} 9 - x^{2} - (- 8 x) d x

簡素化

= \int_{- 1}^{9} 9 - x^{2} + 8 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_{- 1}^{9} 9 d x - \int_{- 1}^{9} x^{2} d x + \int_{- 1}^{9} 8 x d x

\int_{- 1}^{9} 9 d x = 90

\int_{- 1}^{9} x^{2} d x = \frac{730}{3}

\int_{- 1}^{9} 8 x d x = 320

= 90 - \frac{730}{3} + 320

簡素化

90 - \frac{730}{3} + 320 : \frac{500}{3}

= \frac{500}{3}