integral from 0 to 20 of q^2-13q+70

解答

\int_{0}^{20} q^{2} - 13 q + 70 d q

\frac{4400}{3}

十进制

1466.66666 \dots

求解步骤

\int_{0}^{20} q^{2} - 13 q + 70 d q

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_{0}^{20} q^{2} d q - \int_{0}^{20} 13 q d q + \int_{0}^{20} 70 d q

\int_{0}^{20} q^{2} d q = \frac{8000}{3}

\int_{0}^{20} 13 q d q = 2600

\int_{0}^{20} 70 d q = 1400

= \frac{8000}{3} - 2600 + 1400

化简

\frac{8000}{3} - 2600 + 1400 : \frac{4400}{3}

= \frac{4400}{3}

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