integral from 2 to 6 of 4x+12-x^2

解

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

\frac{128}{3}

十進法表記

42.66666 \dots

解答ステップ

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

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

\int_{2}^{6} 12 d x = 48

\int_{2}^{6} x^{2} d x = \frac{208}{3}

= 64 + 48 - \frac{208}{3}

簡素化

64 + 48 - \frac{208}{3} : \frac{128}{3}

= \frac{128}{3}