integral from 0 to 4 of x(0.5-0.125x)

解

\int_{0}^{4} x (0.5 - 0.125 x) d x

1.33333 \dots

解答ステップ

\int_{0}^{4} x (0.5 - 0.125 x) d x

部分積分を適用する

= [0.5 x^{2} (0.5 - 0.125 x) - \int - 0.0625 x^{2} d x]_{0}^{4}

\int - 0.0625 x^{2} d x = - 0.02083 \dots x^{3}

= [0.5 x^{2} (0.5 - 0.125 x) - (- 0.02083 \dots x^{3})]_{0}^{4}

簡素化

[0.5 x^{2} (0.5 - 0.125 x) - (- 0.02083 \dots x^{3})]_{0}^{4} : [0.25 x^{2} - 0.04166 \dots x^{3}]_{0}^{4}

= [0.25 x^{2} - 0.04166 \dots x^{3}]_{0}^{4}

限度を計算する:

1.33333 \dots

= 1.33333 \dots