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

解

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

\frac{11}{6}

十進法表記

1.83333 \dots

解答ステップ

\int_{1}^{2} x^{2} + 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_{1}^{2} x^{2} d x + \int_{1}^{2} x d x - \int_{1}^{2} 2 d x

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

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

\int_{1}^{2} 2 d x = 2

= \frac{7}{3} + \frac{3}{2} - 2

簡素化

\frac{7}{3} + \frac{3}{2} - 2 : \frac{11}{6}

= \frac{11}{6}