find an approximation of the area of the region r under the graph of f

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Jul 25th, 2015

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Thank you for the opportunity to help you with your question!

The Riemann Sum is an approximation of area based on smaller areas under a curve. Here, you have several rectangles underneath the curve, and our task is to find the areas of each of the rectangles, sum them together, and find the approximate area under the curve.

Recall, the area of a rectangle = length x width

According to the x axis, each rectangle has a width of 1/3 units. The number above each rectangle denotes the height on the y axis. So, let's calculate the area of each rectangle:

1/3 * 1.9 = 0.633333...

1/3 * 1.5 = 0.5

1/3 * 1.8 = 0.6

1/3 * 2.4 = 0.8

1/3 * 2.7 = 0.9

1/3 * 2.5 = 0.8333333.....

Summing the areas together, we have:

0.63333333 + 0.5 + 0.6 + 0.8 + 0.9 + 0.833333333 = 4.266666...

Rounded to 2 decimal places, the approximate area under the curve is 4.27 square units.

Please let me know if you need any clarification. I'm always happy to answer your questions.Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 25th, 2015

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