Find U(f, P) and L(f, P) on [1, 4] with where Find R(f, P, c) where c = (3/2,3,4

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Find U(f, P) and L(f, P) on [1, 4] with where Find R(f, P, c) where c = (3/2,3,4) and confirm that L(f, P) le R(f, P, c) le U(f, P). Justify why f is integrable on [1,4]. Let R be the region lying under the graph of f(x). and above the interval [1,4]. Sketch the region R and find its area using partitions with equally spaced points. Use the fundementalTheroem of Calculus to evaluate (Hint: Use the identity sin2x = 1 - cos(2x) / 2 Find a value of c so that 0 le c le pi , and Interpret your results in (a) and (b) in terms of areas; you may want to sketch a graph.

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