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					                               Riemann Sums
Suppose we have the following integral that we wish to approximate:




Right Riemann Sum:




                                     ∆          ∆       …        ∆

Left Riemann Sum:




                                    ∆          ∆      …           ∆
Midpoint Rule:




                                          ∆               ∆       …           ∆

Trapezoid Rule:




                             ∆
                                              2            …    2
                              2


Simpson’s Rule:


                 ∆
                              4           2              …     2              4
                  3



The Definite Integral:

                                  lim             lim         lim       lim            lim

       where ∆           ,              ∆ ,        is the midpoint of the         interval, &   is even for

				
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posted:12/1/2011
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