Let S be the solid of revolution obtained by revolving about the x-axis the bounded region R enclosed by the curve y=x2(1x) and the x-axis. I need help to compute the volume of S using the disk method.

a) Find the values of xx where the curve y=x2(1x) intersects the x-axis.

b) The region R is contained between x=a and x=b with a

c) Let u be a real number in the interval axb. The section of S atx=u is a disk. Written as functions of u, whatare the radius and area of this disk? (please write expressions for the radius and areaas functions of u)

d) The volume of S is given by the integral _a^b f(x)dx, what is f(x)?

e) Find the exact volume of S.