To find a curve whose length over the interval \([1, 2]\) is given by the integral \(\int_{1}^{2} \sqrt{1+\frac{1}{x^{2}}} \, dx\), we need to recall the formula for the arc length of a curve \(y = f(x)\) from \(x = a\) to \(x = b\):
\[
L = \int_{a}^{b} \sqrt{1 +
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