When the graph of y = x2 for 0s x s 2 is rotated about the horizontal line y = L, the volume obtained depends on L: 2n( 15L2 40L+ 48 2 2 dx = 15 (Your answer should contain numbers and L's.) (b) What value of L minimizes the volume in part (a)? (b) What value of L minimizes the volume in part (a)? 4 L (c) When the graph of any continuous function y = f(x) for a sxs b is rotated about the horizontal line y = L, the volume obtained depends on L: V(L) = dx (x)2 dx) + ( -2nL L (Your answers should contain numbers, a's, b's, and/or L's.) (d) What value of L minimizes the volume in part (c)? L = f(x) dx (Your answer should contain numbers, a's, and/or b's. You should recognize the form of this value of L.) 4- 2- y = L