I am currently working on solids of revolution problem. What is given is that $y=2\sqrt{x}$, $y=x$, about the line $x=-2$
I know that $y=2\sqrt{x}$ needs to be solved in terms of $x$ so that it becomes $x=\frac{1}{4}y^2$.
My question is that why does it need to be solved in terms of $x$ and how do I know if something like that needs to be done for a future problem? Is there some indicator?
For this type of problem the washer method seems suitable. Since your axis of revolution is vertical here, using the washer method we would integrate with respect to y, and our inner and outer radii will be the distance from each curve (in terms of y) to the axis of revolution. Let me know if this helps. My advice on these is to always draw a picture and look at several examples to get accustomed to setting up the integrals correctly.