Riemann Sums

The definite integral can be defined as a limit of Riemann sums.


In the script below, enter the function f(x) and the endpoints of the interval [a,b] over which you want to work. When entering f(x), you can use +, -, *, /, ^, ( ), abs(), sin(), cos(), tan(), exp(), log(), log10(), asin(), acos(), atan(), pi, e. Take care to remember the * in all multiplications and to avoid discontinuities. Also, note that here, log() stands for the natural logarithm, while log10() stands for the common logarithm. When entering a and b, you can use integers or decimals. Pressing the "Plot" button will draw the graph of f(x). Then enter the number n of subintervals that [a,b] will be partitioned into, choose whether the partition will regular (all subintervals of the same length) or irregular (lengths chosen by a random number generator), and choose where in the subintervals f will be evaluated. Press the "Calculate" button to show the rectangles corresponding to the Riemann sum and to show the value of the Riemann sum.

     f(x) =

     a =      b =

     n =          Partition:        Sample Pts:  

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