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)
End
L=3
Call findlimit(a:L)
a_exact=9^(1/3)
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)
f=abs(L-3)
a_exact=9^(1/3)
This simple problem has an analytic solution which is the cube root of 9 or 2.08.