Find the volume of the region obtained by revolving the area below about the line x=3.
y = x3, x=2, y=0
Find the moment of inertia of this solid of revolution.
best to use shells here:
v = ∫[0,2] 2πrh dx
where r = 3-x and h = y = x^3
v = 2π∫[0,2] (3-x)x^3 dx
Simply polynomial, so just plug and chug.