integral from 0.25 to 0.5 of 20x^3(1-x)

解

\int_{0.25}^{0.5} 20 x^{3} (1 - x) d x

0.171875

解答ステップ

\int_{0.25}^{0.5} 20 x^{3} (1 - x) d x

定数を除く:

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

= 20 \cdot \int_{0.25}^{0.5} x^{3} (1 - x) d x

拡張

x^{3} (1 - x) : x^{3} - x^{4}

= 20 \cdot \int_{0.25}^{0.5} x^{3} - 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

= 20 (\int_{0.25}^{0.5} x^{3} d x - \int_{0.25}^{0.5} x^{4} d x)

\int_{0.25}^{0.5} x^{3} d x = 0.0146484375

\int_{0.25}^{0.5} x^{4} d x = 0.0060546875

= 20 (0.0146484375 - 0.00605 \dots)

簡素化

= 0.171875