Accuracy of numerical integration in Matlab

I am trying to integrate an analytic function (a composite of sqrt and trig fucntion) on a rectangle area. It has no sigularity point in the area and seems to be a perfect candidate to use dblquad. My question is how to evaluate the accuracy of the numerical value that Matlab provided to me. Without knowing the exact value of the integration, how can one justify the significant-digits? When you are required to give a value with certain digits of precision, you should be able to justify. Is it possible to achieve this given the value is calculated by using Matlab?

Answer 1

[José-Luis]

No, it is not possible. To know exactly how much the answer you get deviates from the true answer, you need to compare to it. In order to compare to it you need to know its value. However, if you use an adaptive integral ( dblquad() is one such) then the error should be inferior or equal to the tolerance you set. The default is 1e-06.

Answer 2

[Jan]

In modern Matlab versions integral2 is more powerful than dblquad: You can determine the relative and absolute tolerance.