integral from 0 to 1 of x^6+x^8

解

\int_{0}^{1} x^{6} + x^{8} d x

\frac{16}{63}

十進法表記

0.25396 \dots

解答ステップ

\int_{0}^{1} x^{6} + x^{8} 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^{6} d x + \int_{0}^{1} x^{8} d x

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

\int_{0}^{1} x^{8} d x = \frac{1}{9}

= \frac{1}{7} + \frac{1}{9}

簡素化

\frac{1}{7} + \frac{1}{9} : \frac{16}{63}

= \frac{16}{63}