# 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) = 3x + 2 from x = 1 to x = 3

Question

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) = 3x + 2 from x = 1 to x = 3

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Step 1

Ypu have asked a question with four sub parts. I have answered the first three sub parts. Please post the balance sub part as separate question.

Width of each rectangle, dx = (x2 – x1) / n = (3 – 1) / 4 = 0.50

Step 2

Part (a)

 x f(x) = 3x + 2 f(x).dx = f(x) x 0.5 1.00 5.00 2.50 1.50 6.50 3.25 2.00 8.00 4.00 2.50 9.50 4.75 Total Area 14.50
Step 3

Part (b)

Right hand rule:

 x f(x) = 3x + 2 f(x).dx = f(x) x 0.5 1.50 6.50 3.25 2.00 8.00 4.00 2.50 ...

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