integral from 0 to 0.5 of 4/3 (1-x^3)

解

\int_{0}^{0.5} \frac{4}{3} (1 - x^{3}) d x

0.64583 \dots

解答ステップ

\int_{0}^{0.5} \frac{4}{3} (1 - x^{3}) d x

定数を除く:

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

= \frac{4}{3} \cdot \int_{0}^{0.5} 1 - x^{3} 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

= \frac{4}{3} (\int_{0}^{0.5} 1 d x - \int_{0}^{0.5} x^{3} d x)

\int_{0}^{0.5} 1 d x = 0.5

\int_{0}^{0.5} x^{3} d x = 0.015625

= \frac{4}{3} (0.5 - 0.015625)

簡素化

\frac{4}{3} (0.5 - 0.015625) : 0.64583 \dots

= 0.64583 \dots