Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the following methods with n=4. f(x)= x² +10 from x = -2 to x = 2 (a) Use left endpoints. (b) Use right endpoints. (c) Average the answers in parts (a) and (b) (d) Use midpoints. (a) The area, approximated using the left endpoints, is
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What is Riemann Sum:
A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use. By dividing the territory into forms that together form a region that is comparable to the region being measured, the area of each of these shapes is computed, and then the total of all of these little areas is determined.
Given:
Given function is . The number of sub-intervals is .
To Determine:
We approximate the area under the curve using left end point and right end point approximation. Then, we determine the average of these values.
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