Shell Method Problem

[RyanJ2]

I think I've done it correctly but I really don't know how to check it. The question states "Use the shell method to set up, but do not evaluate, an integral representing the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4x-x^2 about the line x=6

I had the points of intersection from x=0 to x=2
Shell Radius - I had as 6-x
Shell Height - I put 4x-2x^2

So finally, my integral I had was 2 pi * integral from 0 to 2 [(6-x)(4x-2x^2)]. I was just curious if I did this right and the answer was setup correctly. Note that it doesn't say I need to evaluate it, I just need to set up the integral for it. Thanks!

 

[tkhunny]

Very good. Unfortunately, checking is tricky. As everyone here knows, my favorite method of checking is to do the evaluation and them do it the other way!

Usig Disks (Washers) \(\displaystyle \int_{0}^{4} \left[6-(2-\sqrt{4-y})\right]^2 - (6-\sqrt{y})^{2}\;dy\) -- Same result! Very encouraging.