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monroe17
Find the volume formed by rotating the region enclosed by: y=2sqrt(x) and y=x about the line y=4
The black length represents the outer radius, and the blue one represents the inner radius. Using the disk method, the volume is \[\begin{align*}V&=\pi\int_0^4\left((4-x)^2-(4-2\sqrt x)^2\right)\;dx\\ &=\pi\int_0^4\left((16-8x+x^2)-(16-8\sqrt x+4x)\right)\;dx\\ &=\pi\int_0^4\left(x^2-12x+8\sqrt x\right)\;dx\\ \vdots \end{align*}\]