integral from 0 to 7/6 of 7x-6x^2

解

\int_{0}^{\frac{7}{6}} 7 x - 6 x^{2} d x

\frac{343}{216}

十進法表記

1.58796 \dots

解答ステップ

\int_{0}^{\frac{7}{6}} 7 x - 6 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_{0}^{\frac{7}{6}} 7 x d x - \int_{0}^{\frac{7}{6}} 6 x^{2} d x

\int_{0}^{\frac{7}{6}} 7 x d x = \frac{343}{72}

\int_{0}^{\frac{7}{6}} 6 x^{2} d x = \frac{343}{108}

= \frac{343}{72} - \frac{343}{108}

簡素化

\frac{343}{72} - \frac{343}{108} : \frac{343}{216}

= \frac{343}{216}