integral from 0 to 2 of 1/4 (x^2-7)

解答

\int_{0}^{2} \frac{1}{4} (x^{2} - 7) d x

- \frac{17}{6}

十进制

- 2.83333 \dots

求解步骤

\int_{0}^{2} \frac{1}{4} (x^{2} - 7) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{0}^{2} x^{2} - 7 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

= \frac{1}{4} (\int_{0}^{2} x^{2} d x - \int_{0}^{2} 7 d x)

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

\int_{0}^{2} 7 d x = 14

= \frac{1}{4} (\frac{8}{3} - 14)

化简

\frac{1}{4} (\frac{8}{3} - 14) : - \frac{17}{6}

= - \frac{17}{6}

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