DETAILS SESSCALCET2 5.1.018. (a) Use the following definition to find an expression for the area under the curve y = x from 0 to 3 as a limit. The area A of the region S that lies under the graph of the continuous function fis the limit of the sum of the areas of approximationg rectangles A = lim Rn = lim [f(x1 ) Ax + f(x2)Ax-+ . . . + f (x )4x] O lim (31 3 . 3 n - 0 n 1 = 2 O lim 31 mls n - 0 = 0 A = O lim 31 00 ml O lim m / C n - 0 1 = 1 O lim m / s 1 - 00 = 1 (b) Use the following formula to evaluate the limit in part (a). 13 + 23 + 33 + ... + 13 = n ( n + 1 ) 12