integral from 0 to 2 of (-t^2+3t-2)

解答

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

- \frac{2}{3}

十进制

- 0.66666 \dots

求解步骤

\int_{0}^{2} - t^{2} + 3 t - 2 d t

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} t^{2} d t + \int_{0}^{2} 3 t d t - \int_{0}^{2} 2 d t

\int_{0}^{2} t^{2} d t = \frac{8}{3}

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

\int_{0}^{2} 2 d t = 4

= - \frac{8}{3} + 6 - 4

化简

- \frac{8}{3} + 6 - 4 : - \frac{2}{3}

= - \frac{2}{3}

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