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

解

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

\frac{375}{2}

十進法表記

187.5

解答ステップ

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

\int_{- 2}^{3} 2 x^{4} d x = 110

\int_{- 2}^{3} 4 x^{3} d x = 65

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

\int_{- 2}^{3} 3 d x = 15

= 110 + 65 - \frac{5}{2} + 15

簡素化

110 + 65 - \frac{5}{2} + 15 : \frac{375}{2}

= \frac{375}{2}