yeah, "James" ...
v = ∫[0,4] 2πrh dx
where r = 4-x and h = (32-x^2)-(x^2)
v = ∫[0,4] 2π(4-x)(32-2x^2) dx = 1280π/3
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = 32 − x^2, y = x^2; about x = 4
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