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

解答

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

\frac{375}{2}

十进制

187.5

求解步骤

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

化简

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

= \frac{375}{2}

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