integral from-2 to 0 of (x^2-2x+3)

解

\int_{- 2}^{0} (x^{2} - 2 x + 3) d x

\frac{38}{3}

十進法表記

12.66666 \dots

解答ステップ

\int_{- 2}^{0} x^{2} - 2 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}^{0} x^{2} d x - \int_{- 2}^{0} 2 x d x + \int_{- 2}^{0} 3 d x

\int_{- 2}^{0} x^{2} d x = \frac{8}{3}

\int_{- 2}^{0} 2 x d x = - 4

\int_{- 2}^{0} 3 d x = 6

= \frac{8}{3} - (- 4) + 6

簡素化

\frac{8}{3} - (- 4) + 6 : \frac{38}{3}

= \frac{38}{3}