# approximate the area under the graph of f(x) and above the x-axis using the following methods with n = 4.  (a). use left endpoints, (b). use right end points, (c) average the answers in parts (a) and (b).   (d) use midpoints.  f(x) = 2/x  from   x = 1  to   x = 9

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approximate the area under the graph of f(x) and above the x-axis using the following methods with n = 4.  (a). use left endpoints, (b). use right end points, (c) average the answers in parts (a) and (b).   (d) use midpoints.

f(x) = 2/x  from   x = 1  to   x = 9

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Step 1

Your question has four sub parts. I have answered the first three sub parts. Please post the balance sub part as a separate question.

Step 2

width = dx = (x2 – x1) / n = (9 – 1) / 4 = 2

Step 3

Part (a)

Left endpoints:

 x f(x) = 2 / x f(x).dx = f(x) x 0.5 1.00 2.00 1.00 3.00 0.67 0.33 5.00 0.40 &nbs...

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