Definition: The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim Rn = lim [f(#1)Aa + f(x2)Aæ + ...+ f(xn)A¤]. n00 (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(#) = a from a = 0 to a = 1. A. lim i-1 3 В. lim n00 C. lim n00 D. lim (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula for the sum of cubes helpful: (). n(n + 13 + 23 + 33 + ...+ n 2 The value of the limit is =WI

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