Posted by Macy on Thursday, December 1, 2011 at 11:53am.
first, since it's a square, it does not matter which side is used as the rotational axis.
geometrically, we have a cylinder of height=2, radius=2
v = pi * 2^2 * 2 = 8pi
Analytically,
v = Integral(pi y^2 dx)[0,2]
= Integral(4pi dx)[0,2]
= 4pi x[0,2]
= 8pi
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