Find the surface area of revolution about the y-axis of $y = \sqrt[3]{3x}$ over the interval $0 \le x \le \frac{8}{3}$. Enter your answer in terms of $\pi$ or round to 4 decimal places.
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Step 1: To find the surface area of revolution about the y-axis, we need to use the formula: \[S = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dx}{dy}\right)^2} dy\] where \(a\) and \(b\) are the limits of integration and \(\frac{dx}{dy}\) is the derivative of the Show more…
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