Let x) be a continuous positive function such that Lbdm = K and farm)? d3: = L. Let A be the region enclose-:1 by the curves 3; 2 at], the maxis, :r: = e and .1: = b. An example is illustrated below on the left. If y In this question, we will elevate the region A to different heights above the waxis. This is illustrated above on the right. The region is shifted straight upwards with no Change in shape (\"elevated\") to put its base on the line 3,: = r and the result is assigned the name Ah"). (Vv'e will only consider r 2 O.) (a) \"Find the volume of the solid obtained by rotating A(T) about the :caxis. Your answer should not contain any unevaluated integrals, but it may involve the numbers a", K, and L. (b_ Let V[1') denote the volume found in part (a). Suppose we wish to nd R 2 t] such that VH1?) = 2V(-r). Will we have R <. r or r.="27'," is a consistent prediction irnpossil. justify your answer carefully. f rs="(l" and ti="1." in that taste what the volume of solid obtained by rotating elevated region about. :ruxis>