Question

find the volume of the solid
x=y^2 and x=2y, rotate around y=2

Answer 1

You must first find where x=y^2 and x=2y intersect. Set them equal to each other:
y^2=2y then you solve for y, y^2-2y=y(y-2)=0 so y=0 or y=2, when y=0 we have x=0 (using either of the original equations x=y^2 and x=2y) and when y=2 we have x=4. So we have the points (0,0) and (4,2) the shaded part is what you are rotating about y=2