find the volume of the solid generated by revolving the following region about the y-axis. the region in the first quadrant bounded above by the parabola, y=2x^2, below by the x-axis and on the right by the line x=3

Question

find the volume of the solid generated by revolving the following region about the y-axis.  the region in the first quadrant bounded above by the parabola, y=2x^2, below by the x-axis and on the right by the line x=3

anonymous · Answer

Shell method
height =function
radius=x

anonymous · Answer

i have no clue how to do the shell,washer or disk method....i jujst dont get it

anonymous · Answer

$$2\pi \int _0^32 x^2 *xdx$$

anonymous · Answer

Ok, I will teach you

anonymous · Answer

Let'd do washer first

1) in washer you are adding up bunch  of area of circle
pi r^2

2) in shell 
   you are adding up bunch of cylinder(area of )
      2 Pi  r h  dx  (dx is for thickness of cylinder)

anonymous · Answer

so how do i decipher which i need to do?

anonymous · Answer

You can always do in in either shell or disk(washer)

anonymous · Answer

If we were to try to do this problem in disk method, we would have need the equation in terms of y

anonymous · Answer

okay i gotcha there

anonymous · Answer

so if i do the shell method it would be 2pi*2x^2 xdx and then integrate that?

anonymous · Answer

Yes