How do you find the volume of the region enclosed by the curves #y=x#, #y=-x#, and #x=1# rotated about the y axis?
If rotating about the y-axis, the shell method is your best bet to a quick solution.
hope that helped
Look at the big picture then break it apart into extrusions.
I see it like a (Cylinder-2Cone) instead of a funky shape. So if we find the volume of the cylinder we get
Now we have 2 Cones which are