integral from 0 to 7/2 of-2x^2+7x

解

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

\frac{343}{24}

十進法表記

14.29166 \dots

解答ステップ

\int_{0}^{\frac{7}{2}} - 2 x^{2} + 7 x 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_{0}^{\frac{7}{2}} 2 x^{2} d x + \int_{0}^{\frac{7}{2}} 7 x d x

\int_{0}^{\frac{7}{2}} 2 x^{2} d x = \frac{343}{12}

\int_{0}^{\frac{7}{2}} 7 x d x = \frac{343}{8}

= - \frac{343}{12} + \frac{343}{8}

簡素化

- \frac{343}{12} + \frac{343}{8} : \frac{343}{24}

= \frac{343}{24}