integral from 0 to 1 of pi(x-x^4)

解

\int_{0}^{1} π (x - x^{4}) d x

π \frac{3}{10}

十進法表記

0.94247 \dots

解答ステップ

\int_{0}^{1} π (x - x^{4}) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{1} x - x^{4} 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

= π (\int_{0}^{1} x d x - \int_{0}^{1} x^{4} d x)

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

\int_{0}^{1} x^{4} d x = \frac{1}{5}

= π (\frac{1}{2} - \frac{1}{5})

結合

\frac{1}{2} - \frac{1}{5} : \frac{3}{10}

= π \frac{3}{10}