Question

Find the area of the surface obtained by rotating the curve y x2 0 ≤ x ≤ 2 about the y axis

Answer 1

ds=√1+(dydx)2dx=√1+14(x4−2+1x4)dx

=√14(x4+2+1x4)dx=√122(x2+1x2)2dx

=12(x2+1x2)dx