Question

Use the shell method to find the volume. x=y^2
x=-y y=2 y>=0

Answer 1

\[\int\limits_{2}^{0} 2\pi y \left[ y^2-(-y)\right] dy\]

Answer 2

whoops the 2 is supposed to be on top and zero on bottom

Answer 3

then does that become... \[\int\limits_{0}^{2} 2\pi y^3+y^2/2\]

Answer 4

then do i just plug in 2 and 0 and the answer is 36pi???

Answer 5

if this is a volume of rotation, what is the axis of rotation?

Answer 6

i mean y^4

Answer 7

x axis

Answer 8

so that would change the answer to 16 pi

Answer 9

i am having trouble figuring out what region is it your rotating..... can you shade the portion in the drawing?