integral from 0 to 2 of (2x^2-3x)

解答

\int_{0}^{2} (2 x^{2} - 3 x) d x

- \frac{2}{3}

十进制

- 0.66666 \dots

求解步骤

\int_{0}^{2} 2 x^{2} - 3 x 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}^{2} 2 x^{2} d x - \int_{0}^{2} 3 x d x

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} 3 x d x = 6

= \frac{16}{3} - 6

化简

\frac{16}{3} - 6 : - \frac{2}{3}

= - \frac{2}{3}

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