The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.
x = (y − 2)2, x = 1; about y = 1

Question

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.
x = (y − 2)2,    x = 1;    about y = 1

anonymous · Answer

This is the graph. The region enclosed has to be rotated around the black line

anonymous · Answer

Should I use shell or washer on this?

anonymous · Answer

what's the prob?  you should be a pro at this now!

anonymous · Answer

Haha, I know, I always feel confident, set them up, work them out but then when I turn it in, I always get them wrong.

anonymous · Answer

I initially set it up using shell. I had r(y)=y and h(y)=(y-2)^2

anonymous · Answer

r = (y-1) since you're rotating around the line y = 1.  limits are 1 to 3.  h = (1-(y-2)^2)

anonymous · Answer

Is r = y-1 ?

anonymous · Answer

Ahhh, yes, okay. I had a realization right before you said that, lol

anonymous · Answer

good job!

anonymous · Answer

Yeah. :b But when I worked it out that time I got a negative answer ? 0.0

anonymous · Answer

hold on a sec...|dw:1377645969040:dw|

is this what you got for your integral?