Calculus
posted by Mark on .
Let R be the region bounded by y=−3(x−1)(x−3) and the xaxis. Let S be the solid obtained by rotating R about the yaxis. The volume of S is given by Nπ. What is the value of N?

v = ∫[1,3] 2πrh dx
where r = x and h = y = −3(x−1)(x−3) so
v = ∫[1,3] 2πx(−3(x−1)(x−3)) dx
= 6π ∫[1,3] x^3  4x^2 + 3x dx
= 16π