etermine whether the following statements are true and give an explanation or counter example. Complete parts a through d below. f(b) If the curve y = f(x) on the interval [a,b] is revolved about the y-axis, the area of the surface generated is 2xf(y).1+f'(y) dy. f(a) O A. 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 the function x = g(y). Then the su f(b) OB. area integral becomes (a) 2ngly)/1+g'(y) dy, assuming gly) is positive on the interval [f(a).f(b)). b True. The surface area integral of f(x) when it is rotated about the x-axis on [a,b] is 2f(x)1+ f'(x) dy. To obtain the surface area of the function when it is rotated about the y-axis, change a 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)].