integral from 0 to 20 of x^2-15x+70

解答

\int_{0}^{20} x^{2} - 15 x + 70 d x

\frac{3200}{3}

十进制

1066.66666 \dots

求解步骤

\int_{0}^{20} x^{2} - 15 x + 70 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_{0}^{20} x^{2} d x - \int_{0}^{20} 15 x d x + \int_{0}^{20} 70 d x

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

\int_{0}^{20} 15 x d x = 3000

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

= \frac{8000}{3} - 3000 + 1400

化简

\frac{8000}{3} - 3000 + 1400 : \frac{3200}{3}

= \frac{3200}{3}

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