integral from-1 to 7 of 3x+7-x^2+3x

解

\int_{- 1}^{7} 3 x + 7 - x^{2} + 3 x d x

\frac{256}{3}

十進法表記

85.33333 \dots

解答ステップ

\int_{- 1}^{7} 3 x + 7 - x^{2} + 3 x d x

簡素化

= \int_{- 1}^{7} - x^{2} + 6 x + 7 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}^{7} x^{2} d x + \int_{- 1}^{7} 6 x d x + \int_{- 1}^{7} 7 d x

\int_{- 1}^{7} x^{2} d x = \frac{344}{3}

\int_{- 1}^{7} 6 x d x = 144

\int_{- 1}^{7} 7 d x = 56

= - \frac{344}{3} + 144 + 56

簡素化

- \frac{344}{3} + 144 + 56 : \frac{256}{3}

= \frac{256}{3}