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Problem # 1 For each function f(x) given below, dene F(x) = f: f (t) dt. 1) Is F(x) an antiderivative of f(x)? 2) Plot f(x) and F(x) in the same window for XE [(1, b]. 3) How is F(x) related to the area between f(x) and the xaxis on[a, b]? (a) f(x)=i a=l,b=10 ' x2 (b) f(x)=sinx, a=0,b=11r Problem # 2 The integral f 01 x2 dx represents the area A of a region in the rst quadrant. (a) Find the exact area A using integral. (b) Approximate A, using the right-hand method and the following partitions: 1.n=10 2.n=100 3.n=1000 Which of these three will give the best answer? (c) Work this problem by using the Maple command \"ApproximateInt\". How does this result compare to the one obtained in (a)