Show all work 1. We will use the following definition to calculate the exact arca under a curve. 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 approximative rectangles: n Arca = A = lim Rn = lim > f(x.)Ar = lim [f(x1 )Ar + f(x2)Ar + ... + f(In)Ax] n-+00 k=1 12-+00 (a) Use the definition of arca given above to write a limit that is equal to the arca under the graph of f(x) = 12 - 4x + 4 from = = 0 to r = 2. Do not evaluate the limit yet. (b) Evaluate the limit in part (a) using these two formulas, both found in Theorem 3 of Appendix F of your book. 12 + 22 + 32 + ... + n2 _ n(n + 1) (2n + 1) n(n + 1) 1+2+3+ . . . +n= 6 2 (c) The answer for part (b) should represent the area under f(x) between r = 0 and c = 2. Explain briefly why this limit represents the arca under f