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

解答

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

- 1

求解步骤

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

提出常数:

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

= - 2 \cdot \int_{1}^{2} \frac{1}{x ^{2}} d x

使用幂法则

= - 2 [- \frac{1}{x}]_{1}^{2}

带入上下限计算后得:

\frac{1}{2}

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

化简

= - 1

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