integral from-1 to 2 of (5x^3+2x^2-x)

解

\int_{- 1}^{2} (5 x^{3} + 2 x^{2} - x) d x

\frac{93}{4}

十進法表記

23.25

解答ステップ

\int_{- 1}^{2} 5 x^{3} + 2 x^{2} - x 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

= \int_{- 1}^{2} 5 x^{3} d x + \int_{- 1}^{2} 2 x^{2} d x - \int_{- 1}^{2} x d x

\int_{- 1}^{2} 5 x^{3} d x = \frac{75}{4}

\int_{- 1}^{2} 2 x^{2} d x = 6

\int_{- 1}^{2} x d x = \frac{3}{2}

= \frac{75}{4} + 6 - \frac{3}{2}

簡素化

\frac{75}{4} + 6 - \frac{3}{2} : \frac{93}{4}

= \frac{93}{4}