integral from 0 to 1 of 2-x-x^2

解答

\int_{0}^{1} 2 - x - x^{2} d x

\frac{7}{6}

十进制

1.16666 \dots

求解步骤

\int_{0}^{1} 2 - x - x^{2} 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}^{1} 2 d x - \int_{0}^{1} x d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} 2 d x = 2

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= 2 - \frac{1}{2} - \frac{1}{3}

化简

2 - \frac{1}{2} - \frac{1}{3} : \frac{7}{6}

= \frac{7}{6}

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