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Problem 75 Hard Difficulty

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

$$ \frac{1}{m(m + 1)} = \frac{1}{m} - \frac{1}{m + 1} $$

Answer

$\frac{1}{2}$

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Video Transcript

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.