Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.\\ $x = \sqrt{y} - 9y$, $1 \le y \le 4$ dy = 26.1725
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Step 1: The arc length of a curve $x = f(y)$ from $y = a$ to $y = b$ is given by the integral $$L = \int_a^b \sqrt{1 + \left(\frac{dx}{dy}\right)^2} dy$$ In this problem, $x = \sqrt{y} - 9y$, $a = 1$, and $b = 4$. Show more…
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