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# Find $\displaystyle \int^2_1 x^{-2} \,dx$. $Hint:$ Choose $x_i^*$ to be the geometric mean of $x_{i - 1}$ and $x_i$ (that is, $x_i^* = \sqrt{x_{i - 1}x_i}$) and use the identity$$\frac{1}{m(m + 1)} = \frac{1}{m} - \frac{1}{m + 1}$$

## $\frac{1}{2}$

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Given what we know about the Riemann. Some we know the integral from wonder, too of one over expert detox is equivalent to the limit as an approaches infinity a of one. Therefore, we know the limit as that approaches infinity. This is equivalent to 1/2.

Integrals

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