Question

1. Given the function f(x)= (x-3)2+c, g(x)=(x-1)3+1, and h(x)= - (x-5)3+1 on the interval [0,6] .
A.) If f(x) divides the shaded region into two equal parts R and S, find the value of C.
B.) Find the volume generated by revolving the shaded region R about the x – axis.
C.) Find the volume generated by revolving the shaded region S about the x – axis.
D.) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x – axis are squares. Find the volume of the solid.
E.) The region S is the base of a solid. For this solid, the cross sections perpendi