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Example Estimate the area under the graph of f(r) = 1/x from 2 = 1 to x = 4 using six pproximating rectangles and Ax = 20= = \\, where [a, b] = [1, 4] and n = 6. Mark the points to, *1; $2, ...;2's which divide the interval (1, 4] into six subintervals of equal length on che following axis: Fill in the following tables: 20 = 1 21 = 3/2 22 = 2 23 = 5/2 $4 = 3 25 = 7/2 26=4 f(i) = 1/24 (a) Find the corresponding right endpoint approximation to the area under the curve y = 1/r on the interval [1, 4]. Ro = f(x1)Ax + f(22) Ax + f(23)Ax + f(a )Ax + f(25)Ax + f(26)4x (b) Find the corresponding left endpoint approximation to the area under the curve y = 1/r on the interval [1, 4]. Le = f(:o) Aa: + f(:1) Ax + f (8:2) Ax + f(3) ; + f(:) As: + f(:15) AxExample 2: Find the area under the curve: y = J35 over [0,4] using the midpoint method w/ n = 8 Example 3: Find the area under the curve: f(x) = x - Zlnx [1,5] using R (n = 5); L01 = 5) and M(n = 5)