Determine whether the following statements are true and give an explanation or counter example. Complete parts a through d below. f(b) a. If the curve y = f(x) on the interval [a,b] is revolved about the y-axis, the area of the surface generated is S 2of(y) 17+ f(y)? dy. fa) OA. b True. The surface area integral of f(x) when it is rotated about the x-axis on [a,b] is ſzaf(x)/1+f'(x)? dy. To obtain the surface area of the function when it is rotated about the y-axis, change the limits of integration to f(x) evaluated at each endpoint and integrate with respect to y. This is assuming f(y) is positive on the interval [f(a) f(b)] OB. False. To obtain the surface area integral of f(x) when it is rotated about the y-axis on [a,b], the function y = f(x) must be solved for x in terms of y. This yields f(b) the function x = g(y). Then the surface area integral becomes $ 279(9)/1+gʻ(v)dy, assuming gly) is positive on the interval [f(a) f(b)]. fla)