Let R1 be the region bounded by y = x2, y = 0, and x = b, where b > 0. Let R2 be the region bounded by y = x2, x = 0, and y = b2.
(a) Is there a value of such that R1 and R2 have the same area?
(b) Is there a value of such that R1 sweeps out the same volume when rotated about the x-axis and the -axis?
(c) Is there a value of such that R1 and R2 sweep out the same volume when rotated about the -axis?
(d) Is there a value of such that R1 and R2 sweep out the same volume when rotated about the y-axis?