integral from 4.9 to 5.1 of x(5x-24.5)

解

\int_{4.9}^{5.1} x (5 x - 24.5) d x

0.50333 \dots

解答ステップ

\int_{4.9}^{5.1} x (5 x - 24.5) d x

部分積分を適用する

= [0.5 x^{2} (5 x - 24.5) - \int 2.5 x^{2} d x]_{4.9}^{5.1}

\int 2.5 x^{2} d x = 0.83333 \dots x^{3}

= [0.5 x^{2} (5 x - 24.5) - 0.83333 \dots x^{3}]_{4.9}^{5.1}

拡張

0.5 x^{2} (5 x - 24.5) - 0.83333 \dots x^{3} : 1.66666 \dots x^{3} - 12.25 x^{2}

= [1.66666 \dots x^{3} - 12.25 x^{2}]_{4.9}^{5.1}

限度を計算する:

0.50333 \dots

= 0.50333 \dots