So who wants to help me?

Question

luigi0210 · Answer

Determine the volume of the solid obtained by rotating the region bounded by x=(y-2)^2 and y=x about the line y=-1.

tkhunny · Answer

Have you selected your favorite method?

luigi0210 · Answer

I have never understood volume.. so no.

tkhunny · Answer

Have you met the Theorem of Pappus?  This could be very useful, here.

luigi0210 · Answer

Nope, I'm just a first semester calculus student.

tkhunny · Answer

Too bad.  Anyway, let's first find out what area is enclosed by the two curves.  We'll need points of intersection for that.  Please find them and report them.

luigi0210 · Answer

y=(y-2)^2
y=y-4x+4
0=y-5x+4
0=(y-4)(y-1)
At y=1and 4

tkhunny · Answer

Very good.  Unfortunately, this one is a little annoying.  If we use disks/washers or shells, we'll have to do it in two pieces.  Are you SURE you don't have a preference?  Maybe you've seen only one way or the other?

tkhunny · Answer

Well, I hope @loser66 can guide you from here.  I have to go fix my garage before the sun sets on the East Coast of the USof A.

luigi0210 · Answer

Alright.. thank you! @tkhunny

luigi0210 · Answer

attachment

loser66 · Answer

attachment

tkhunny · Answer

Are we still working on this!