integral from-2 to 5 of-2x^2+6x+20

解答

\int_{- 2}^{5} - 2 x^{2} + 6 x + 20 d x

\frac{343}{3}

十进制

114.33333 \dots

求解步骤

\int_{- 2}^{5} - 2 x^{2} + 6 x + 20 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} 2 x^{2} d x + \int_{- 2}^{5} 6 x d x + \int_{- 2}^{5} 20 d x

\int_{- 2}^{5} 2 x^{2} d x = \frac{266}{3}

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

\int_{- 2}^{5} 20 d x = 140

= - \frac{266}{3} + 63 + 140

化简

- \frac{266}{3} + 63 + 140 : \frac{343}{3}

= \frac{343}{3}

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