Question: Let g(x) = (1 - 2x)(x - 3), and let A be the region enclosed by y = g(x), x = 1, x = 2, and y = -1.
If we revolve the region A about x-axis we obtain a solid. i. Find the volume of this solid. ii. Find its total surface area.
My Attempt: I have already drawn a graph and calculated the volume. For the volume, although a bit tedious, I expanded the function so that it's easier to integrate. But for the surface area, I have absolutely no clue on how to do it. I know its formula, but apparently there's no way of simplifying it. I think it may have something to do with trigonometric substitution? Can anyone please give me clues on how to approach it?