integral from-2 to 1 of (5x^2-7x+3)

解

\int_{- 2}^{1} (5 x^{2} - 7 x + 3) d x

\frac{69}{2}

十進法表記

34.5

解答ステップ

\int_{- 2}^{1} 5 x^{2} - 7 x + 3 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}^{1} 5 x^{2} d x - \int_{- 2}^{1} 7 x d x + \int_{- 2}^{1} 3 d x

\int_{- 2}^{1} 5 x^{2} d x = 15

\int_{- 2}^{1} 7 x d x = - \frac{21}{2}

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

= 15 - (- \frac{21}{2}) + 9

簡素化

15 - (- \frac{21}{2}) + 9 : \frac{69}{2}

= \frac{69}{2}