**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.