integral from 0 to 3/7 of 3x-7x^2

解

\int_{0}^{\frac{3}{7}} 3 x - 7 x^{2} d x

\frac{9}{98}

十進法表記

0.09183 \dots

解答ステップ

\int_{0}^{\frac{3}{7}} 3 x - 7 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{3}{7}} 3 x d x - \int_{0}^{\frac{3}{7}} 7 x^{2} d x

\int_{0}^{\frac{3}{7}} 3 x d x = \frac{27}{98}

\int_{0}^{\frac{3}{7}} 7 x^{2} d x = \frac{9}{49}

= \frac{27}{98} - \frac{9}{49}

簡素化

\frac{27}{98} - \frac{9}{49} : \frac{9}{98}

= \frac{9}{98}