(a) use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 (b) the following formula for the sum of the cubes of the first n integers is proved in appendix e. use it to evaluate the limit in part (a). 13 + 23 + 33 + + n3 = n(n + 1) 2 2