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Rectangular Approximation (LRAM, RRAM, MRAM)

Author:Rachel Burris, bkinnell
Approximate the area under a curve with the rectangular approximation method. Enter a function, f(x), change the limits x1 and x2, and then select a right-hand, left-hand, or midpoint rectangular approximation technique. Change n to adjust the number of rectangles.

Consider MRAM, RRAM, and LRAM with n=4 for the function . (You can compare them together by checking two or three of the boxes at a time) Which one do you think will give the most precise estimate? Will any of them estimate the area under this curve equally? Explain your answer.

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This time change the function in the f(x) box to be "20/x". Now which RAM will overestimate the area under the curve when ? Which one will underestimate it?

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Change the function in the f(x) box to be "sqrt(10x)". Now which RAM will overestimate the area under the curve? Which one will underestimate it?

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Use the slider to change the value of n. As n increases, what do you observe?

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What generalizations can you make about how well LRAM, RRAM, and MRAM estimate different types of curves?

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