Hello. I am working on problem set 7 #4c2 (solids of revolution by shell method). I am told to "Find the volume of the region 0 ≤ y ≤ x2, x ≤ 1 revolved around the y-axis." I am having trouble figuring out the graph from the given statements. The graph provided in the answers has a "blip" between ~0 and ~1/3 on the x axis where y becomes negative and I don't understand how y can be negative if it is between 0 and x^2. Thanks for your help.

Question

Hello.  I am working on problem set 7 #4c2 (solids of revolution by shell method).  I am told to "Find the volume of the region 0 ≤ y ≤ x2, x ≤ 1 revolved around the y-axis."  I am having trouble figuring out the graph from the given statements.  The graph provided in the answers has a "blip" between ~0 and ~1/3 on the x axis where y becomes negative and I don't understand how y can be negative if it is between 0 and x^2.  Thanks for your help.

anonymous · Answer

I am going to close this problem.  I am not sure why the provided graph looks like it does but setting y=x^2 and solving provides the correct answer.

phi · Answer

***The graph provided in the answers has a "blip" ***

it looks like "artistic license".  The curve they show is not y=x^2.   But all they are trying to show (I think) is the "set-up".