Question
Asked May 10, 2019

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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Expert Answer

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)

Please see the table below:

xf(x) = 3x + 2f(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:

xf(x) = 3x + 2f(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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Math

Calculus

Integration

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