Contents - Index

Finding a Limit of Integration


The algorithms used in EES Integral function for numerical integration do not allow EES to directly solve for a limit of integration.  For example, the following equation would produce an error in EES.


3=integral(x^2 ,x, 0, a) 


It is possible, however, to solve this problem in several other ways.  Perhaps the simplest solution is to use a Subprogram in which the limit, (variable a in this problem) is provided as a parameter.  The method is illustrated in the following equations.


SubProgram FindLimit(a:L)

      L=integral(x^2, x, 0, a)




Call FindLimit(a:L)



Another way to solve this problem is to reformulate the problem to be an optimization problem and use the Min/Max command.  In this case,  EES will adjust variable a so as to minimize an objective function.  The method is illustrated in the following equations.


L=integral(x^2, x, 0, a)




This simple problem has an analytic solution which is the cube root of 9.