Question
Find the exact area of the surface obtained by rotating the curve about the x-axis.$ x = \frac{1}{3} (y^2 + 2)^{\frac{3}{2}} $ , $ 1 \le y \le 2 $
Step 1
The derivative of $x = \frac{1}{3} (y^2 + 2)^{\frac{3}{2}}$ with respect to $y$ is given by the chain rule as $dx/dy = \frac{1}{2} (y^2 + 2)^{\frac{1}{2}} \cdot 2y = y(y^2 + 2)^{\frac{1}{2}}$. Show more…
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