integral from-1 to 4 of (5x^4-8x^3+6)

解答

\int_{- 1}^{4} (5 x^{4} - 8 x^{3} + 6) d x

545

求解步骤

\int_{- 1}^{4} 5 x^{4} - 8 x^{3} + 6 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{4} 5 x^{4} d x - \int_{- 1}^{4} 8 x^{3} d x + \int_{- 1}^{4} 6 d x

\int_{- 1}^{4} 5 x^{4} d x = 1025

\int_{- 1}^{4} 8 x^{3} d x = 510

\int_{- 1}^{4} 6 d x = 30

= 1025 - 510 + 30

化简

= 545