integral from-1 to 0 of (x^2-4x+7)

解

\int_{- 1}^{0} (x^{2} - 4 x + 7) d x

\frac{28}{3}

十進法表記

9.33333 \dots

解答ステップ

\int_{- 1}^{0} x^{2} - 4 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}^{0} x^{2} d x - \int_{- 1}^{0} 4 x d x + \int_{- 1}^{0} 7 d x

\int_{- 1}^{0} x^{2} d x = \frac{1}{3}

\int_{- 1}^{0} 4 x d x = - 2

\int_{- 1}^{0} 7 d x = 7

= \frac{1}{3} - (- 2) + 7

簡素化

\frac{1}{3} - (- 2) + 7 : \frac{28}{3}

= \frac{28}{3}