# Riemann Left and Right Hand Sums

Give the following table of values determine by the empirical (ie: the Riemann left and right hand sums) method the area under the function between X=0 and X=70. (hint: use n=7)

X 0 10 20 30 40 50 60 70

Y 700 400 300 400 700 1200 1900 2800

A. Graph the function over these x values and explain in your own words what the relationship means. Is it an additive function?

B. Compute the left and right hand areas of the five rectangles and superimpose these rectangles on the graph or the data table.

C. Approximate the true area and determine a function statement or equation that best describes the relationship between the area and x values.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

(a) According to the data given from the table, we graph the function as below.

From the graph, the function is not an additive function, but is more like a quadratic function.

(b) Now we calculate the left and right Riemann Sum with .

The left Riemann sum is

The right Riemann sum is

(c) From (a), I guess it is a quadratic function. I assume the equation is

Then we have .

We also have

Therefore, the equation is .

So the corresponding area under the curve is

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