I've been given the graph y = $4x - 4x^2$ that has been bound by the x-axis. I've been asked to find the volume of Solid of Revolution about the y-axis using the disc method.
In order to find the inner and outer radii of the disc/washer, I've gotten the question in terms of x as follows:
x = $-\frac{\sqrt{-y+1}-1}{2},\:x=\frac{\sqrt{-y+1}+1}{2}$
Where I'm getting stuck is in knowing which one of these to use for the inner and outer radii. My guess was that I'd use the right side of the graph, given by $x=\frac{\sqrt{-y+1}+1}{2}$ as the outer radius, and subtract that from the left side of the graph, given by x = $-\frac{\sqrt{-y+1}-1}{2}$, but I'm not too sure.
I was wondering if I could get a few pointers on how to approach finding the inner and radii of each washer.
You are on the right track, the set up should be
$$\int_{0}^{1} \pi [R_2(y)^2-R_1(y)^2)]\,dy=\int_{0}^{1} \pi\left[\left(\frac{1+\sqrt{1-y}}{2}\right)^2-\left(\frac{1-\sqrt{1-y}}{2}\right)^2\right]\,dy$$