find the area of the surface generated by revolving about x-axis the upper half of the ellipse 4x^2 + 16y^2 = 64

Answer 1

A good discussion is found at

http://math.stackexchange.com/questions/1379341/how-to-find-the-surface-area-of-revolution-of-an-ellipsoid-from-ellipse-rotating

google is your friend.