(a) When the graph of y = x2 for D s x S 2 is rotated about the horizontal line y = LI the volume obtained depends on L: 2 2 3231 (16m) . 2 V(L)=f 27L d: +27I:L o 7r(x ) X 5 3 (Your answer should contain numbers and L's.) (b) What value of L minimizes the volume in part (a)? i \"3 u! (c) When the graph of any continuous function y = f(x) for a g X g b is rotated about the horizontal line 1.! = L, the volume obtained depends on L: my 2 [b21000 ,1)de :l \"5 ., )(fx)2dx)+( '3'\"? )lffi")d")+ \"Lab\"l I (Your answers should contain numbers, a's, b's, and/or L's.) (d) What value of L minimizes the volume in part (c)? H )(fm) (Your answer should contain numbers, a's, and/or b's. You should recognize the form of this value of L.)