integral from-1 to 6 of |11x^2-x^3-24x|

解

\int_{- 1}^{6} 11 x^{2} - x^{3} - 24 x d x

\frac{1325}{12}

十進法表記

110.41666 \dots

解答ステップ

\int_{- 1}^{6} 11 x^{2} - x^{3} - 24 x d x

絶対数を排除する

= \int_{- 1}^{0} 11 x^{2} - x^{3} - 24 x d x + \int_{0}^{3} - 11 x^{2} + x^{3} + 24 x d x + \int_{3}^{6} 11 x^{2} - x^{3} - 24 x d x

\int_{- 1}^{0} 11 x^{2} - x^{3} - 24 x d x = \frac{191}{12}

\int_{0}^{3} - 11 x^{2} + x^{3} + 24 x d x = \frac{117}{4}

\int_{3}^{6} 11 x^{2} - x^{3} - 24 x d x = \frac{261}{4}

= \frac{191}{12} + \frac{117}{4} + \frac{261}{4}

簡素化

\frac{191}{12} + \frac{117}{4} + \frac{261}{4} : \frac{1325}{12}

= \frac{1325}{12}