How do you use the shell method to compute the volume of the solid obtained by rotating the region in the first quadrant enclosed by the graphs of the functions #y=x^2# and #y=2# rotated about the y-axis?
We will rotate the area bounded by the two curves and the y-axis. In other words we will restrict ourselves to the region in the first quadrant.
Since we a rotating around the y axis using the method of shells
we integrate with respect to x.
Now find where the curves intersect.
Therefore the interval over which we integrate is
Our representative radius will be some value of
Our representative cylinder height is
Using method of shells, the integral for the volume is