integral from-2 to 5 of (x^2+6x+8)

解答

\int_{- 2}^{5} (x^{2} + 6 x + 8) d x

\frac{490}{3}

十进制

163.33333 \dots

求解步骤

\int_{- 2}^{5} x^{2} + 6 x + 8 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}^{5} x^{2} d x + \int_{- 2}^{5} 6 x d x + \int_{- 2}^{5} 8 d x

\int_{- 2}^{5} x^{2} d x = \frac{133}{3}

\int_{- 2}^{5} 6 x d x = 63

\int_{- 2}^{5} 8 d x = 56

= \frac{133}{3} + 63 + 56

化简

\frac{133}{3} + 63 + 56 : \frac{490}{3}

= \frac{490}{3}

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