integral from-2 to 6 of (4x)-(x^2-12)

解

\int_{- 2}^{6} (4 x) - (x^{2} - 12) d x

\frac{256}{3}

十進法表記

85.33333 \dots

解答ステップ

\int_{- 2}^{6} 4 x - (x^{2} - 12) d x

簡素化

= \int_{- 2}^{6} 4 x - x^{2} + 12 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}^{6} 4 x d x - \int_{- 2}^{6} x^{2} d x + \int_{- 2}^{6} 12 d x

\int_{- 2}^{6} 4 x d x = 64

\int_{- 2}^{6} x^{2} d x = \frac{224}{3}

\int_{- 2}^{6} 12 d x = 96

= 64 - \frac{224}{3} + 96

簡素化

64 - \frac{224}{3} + 96 : \frac{256}{3}

= \frac{256}{3}