Can someone help me solve this volume problem? I think it's by the cylindrical shell method.

Question

logando · Answer

attachment

eazye_the_best · Answer

ummm give me a second

eazye_the_best · Answer

hold on my computer is lagging out

irishboy123 · Answer

you should draw this every time, before you start

logando · Answer

I did, but the reason I'm confused is that we're rotating the region around itself. The region is from x=0 to x=2, but we're rotating it around x=1, so I don't know if the radius would be (1-x) or (x-1) and am I supposed to halve the integral?

irishboy123 · Answer

assuming it is not a bad question, i would be tempted to rotated the area $1 \le x \le 2$ about $x = 1$


but i definitely see your point.  rogue question!

logando · Answer

Haha yeah, my professor's a bit tough

anonymous · Answer

I think @IrishBoy123 has the right idea, though you might want to include the volume generated by revolving the region the left of $x=1$ too for good measure. That is, compute the volumes of both solids generated from the regions over $[0,1]$ and $[1,2]$ individually, then add them together. Unless your prof explicitly stated at some point that self-intersecting solids aren't allowed?