g(x)= √(19x) = upper curve f(x)= 0.2x^2 = lower curve Firstly, I found the point of intersection, which would later give the upper values for x and y. x=7.802 y=12.174 Then I found the area under g(x) and took away the area under f(x) to get the area between the curves. 31.67 units^2 This is where I will include the equations so it is easy to see if I have done it right. VolX = ∫π[(g(x)^2)-(f(x)^2)] dx (The outer line squared minus the inner line squared) Putting in my values for g(x)^2 and f(x)^2 g(x)^2 = 19x f(x)^2 = 0.04x^4 Between 0 and 7.802 this gave me a volume of 1090.133 units^3 VolY = ∫π[(f(y)^2)-(g(y)^2)] dy This time the line that was the inner in relation to the x axis becomes the outer and vice versa. f(y)^2 = 5y g(y)^2 = (y^4)/361 Solving this integral between 0 and 12.174 gave me a volume of 698.59 units^3 Next, the task was to find the centroid of the area, specifically using the theorem of pappus. This task is given a distinction mark, however after looking at it it seems quite simple and I'm not sure if I am missing something. VolX = Shaded area x 2π(ybar) So (1090.133)/(31.67x2π) = ybar = 5.478 Then I haven't done xbar yet but I would think that I just do the same with VolY = Shaded area x 2π(xbar) Is there anything that you can see that I might have missed that makes the last part more difficult? Thanks!