integral from-1 to 4 of (2x^4+5x^3-x+5)

解

\int_{- 1}^{4} (2 x^{4} + 5 x^{3} - x + 5) d x

\frac{2985}{4}

十進法表記

746.25

解答ステップ

\int_{- 1}^{4} 2 x^{4} + 5 x^{3} - x + 5 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}^{4} 2 x^{4} d x + \int_{- 1}^{4} 5 x^{3} d x - \int_{- 1}^{4} x d x + \int_{- 1}^{4} 5 d x

\int_{- 1}^{4} 2 x^{4} d x = 410

\int_{- 1}^{4} 5 x^{3} d x = \frac{1275}{4}

\int_{- 1}^{4} x d x = \frac{15}{2}

\int_{- 1}^{4} 5 d x = 25

= 410 + \frac{1275}{4} - \frac{15}{2} + 25

簡素化

410 + \frac{1275}{4} - \frac{15}{2} + 25 : \frac{2985}{4}

= \frac{2985}{4}