Find the length of the curve $y = x^2 - \frac{1}{8}\ln(x)$ for $1 \le x \le 3$.
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Step 1: The arc length of a curve $y = f(x)$ from $x = a$ to $x = b$ is given by the formula: $$L = \int_a^b \sqrt{1 + (f'(x))^2} dx$$ In this case, $f(x) = x^2 - \frac{1}{8}\ln(x)$, $a = 1$, and $b = 3$. Show more…
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