Use the Shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 81 - x$^2$, y = 0
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The formula for the volume of a solid of revolution using the shell method is: $$V = 2\pi \int_{a}^{b} x f(x) dx$$ where $f(x)$ is the height of the shell, $x$ is the radius of the shell, and $a$ and $b$ are the limits of integration. Show more…
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