Let S be the surface obtained by rotating the smooth curve 3,: = at}, a 5 a: 5 b, about the :caxis, where fl:1') 2 U. (a) Show that the vector function as. a) = xi + fix) were} + no sinwifc is a parametrization of S. where B is the angle of rotation around the :tards [see the accompanying gure]. (b) Use the surface area formula for parametrized surfaces derived in class to show that the surface area of this surface of revolution is given by in A: f 2wf(s)\\/1+[f'{:r}]3dm