integral from 0 to 1 of (x^2+x^6)

解

\int_{0}^{1} (x^{2} + x^{6}) d x

\frac{10}{21}

十進法表記

0.47619 \dots

解答ステップ

\int_{0}^{1} x^{2} + 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_{0}^{1} x^{2} d x + \int_{0}^{1} x^{6} d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} x^{6} d x = \frac{1}{7}

= \frac{1}{3} + \frac{1}{7}

簡素化

\frac{1}{3} + \frac{1}{7} : \frac{10}{21}

= \frac{10}{21}