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(x1)Ax + f(xæ2)Ar+.+f(xn)Az] no0 no0 (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x³ from x = 0 to x = 2. 64 25 TH00 TL i=l A. lim 1 В. lim 64 C. lim 64 D. lim n00 n6 i=1 (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula helpful: n2(n + 1)²(2n² + 2n – 1) 15 + 25 + 35+..+n³ = %3D 12 Value of limit = LIWIWIWI

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