CALC 2

Question

Using rectangles each of whose height is given by the value of the function at the midpoint of the​ rectangle's base​ (the midpoint​ rule), estimate the area under the graph of the following​ function, using first two and then four rectangles. f(x) = 2/x between x=5 and x=9

Answer 1

I did the 4 rectangle part of the question.
You do the easier part with only 2 rectangles

Each rectangle has a width of 1 unit and the midpoint values are
5.5, 6.5, 7.5, and 8.5
f(5.5) = 2/5.5 = .3636
f(6.5) = 2/6.5 = .3077
f(7.5) = .2667
f(8.5) = .2353

appr area = (1)(.3636 + .3077 + .2667 + .2353) = 1.1733

(actual area by calculus) = 1.1756