Consider the given curves to do the following.
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = -4.
I'm getting 302pi/60
I set it up as 2pi*(the integral from 0 to 1) of (y-4)((y^2)-(y^.5))dy
sketch a representative horizontal rectangle within the given region.
the right end of the rectangle is
the left end of the rectangle is
the height of the rectangle is (right - left) = and the thickness of the rectangle is
the rectangle is a distance of above the x-axis
the vertical distance from the rectangle to the line is , so the radius of revolution is
the volume of a single shell is ...
dV = (radius of revolution)(height of rectangle)(rectangle thickness)