Try integratinf from 0-4 and multiply by another constant of 2.
I am getting a bit confused here.. the question asks to find the volume of the solid that results from rotating around the line .
My setup is this:
but when i integrate and substitute i cant get values for the negative lower limit.. what's my error?
we want the volume the green volume as the picture shows us
the function is
to make it easier let new x=x+4 to make the volume around the y-axis
so the new question will be
and x=-2 around the y-axis
so the picture will be like this
and we want the volume revolution around y-axis
note that is not all the curve if we calculate the volume for y it will be half of what we need since it is symmetric
the volume of this around y-axis
multiply it with 2 to get what you need
limits is x=-4 and x=-2 since the region is bounded by this two lines
Cylindrical shell says the volume generated by revolving a region bounded above by a continuous function and from the left by the line x=a and from the right by the line x=b given by
in the second way I used washers
look to the picture
if we look to the two curves
want the volume bounded by this to curves revolving around y-axis
find the point of intersection
so the volume will be