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Riemann Sums MRAM. Madi Day and Janelle Trieu Period 1 &5. Midpoint

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## Riemann Sums MRAM

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**Riemann SumsMRAM**Madi Day and Janelle Trieu Period 1 &5**Midpoint**In the picture above the width of each rectangle will be 1/2 and the length (height) will be the value of the function evaluated at the midpoint of the subinterval corresponding to that rectangle. In this case the area of the region will be approximated by What is MRAM? • MRAM : Midpoint Rectangular Approximation Method • It is used to find an approximation of the area under a curve • How is it done you ask? • First Graph your function • Secondly divide your graph into sub-intervals • Find the midpoints of each of these intervals, on the graph • (The height of your rectangles is based off these points…) • (Plug the midpoint into the formula given to find the Y value, the point on the graph which gives you the height) • Draw your rectangles • Find the area of each rectangle and add them together • What if there is no function? But a table instead? • Sometimes tables with points are given instead of a function • First you graph the points and connect them • Then you find the midpoint between the points given and estimate the height • Draw your rectangles and find the area • Add the areas together and find the total area**Examples:**• http://www2.seminole.cc.fl.us/lvosbury/CalculusI_Folder/RiemannSumDemo.htm • http://www.ltcconline.net/greenl/courses/105/Antiderivatives/numint.htm • http://tutorial.math.lamar.edu/Classes/CalcII/ApproximatingDefIntegrals.aspx • Good website: http://archives.math.utk.edu/visual.calculus/4/index.html**Tip!**• Subgroups should be .25 . 5 .75 etc. those are easiest • Also, the smaller the width of the rectangles the more exact the answer

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