The region under the curves #y=xe^(x^3), 1<=x<=2# is rotated about the x axis. How do you find the volumes of the two solids of revolution?

Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"