integral from 1 to 6 of (x^2-7x+6)

解

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

- \frac{125}{6}

十進法表記

- 20.83333 \dots

解答ステップ

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

\int_{1}^{6} x^{2} d x = \frac{215}{3}

\int_{1}^{6} 7 x d x = \frac{245}{2}

\int_{1}^{6} 6 d x = 30

= \frac{215}{3} - \frac{245}{2} + 30

簡素化

\frac{215}{3} - \frac{245}{2} + 30 : - \frac{125}{6}

= - \frac{125}{6}