I want to make sure I understand and vizualise it right - Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x, y = 0, x = 2, and x=4 about the line x = 1 ;
the outer radius would be (4-y) - 1 = 3 - y, and the inner radius (2-y) - 1 = 1 - y
The area A(y) = pi(R^2 - r^2) = pi(3-y)^2 - pi(1-y)^2 = pi[(9 - 6y + y^2) - (1 - 2y + y^2)] = pi(8 - 4y) which I need to integrate from 0 to 4, right? It's
confusing and I am not sure I get the right result - maybe it's something in the area that I'm missing...