Step 1 :The integral is evaluated from 0 to 0, which means the lower and upper limits of the integral are the same.
Step 2 :In such cases, the integral of any function over an interval of zero width is always 0.
Step 3 :Therefore, the integral of \(2+\sqrt{81-x^{2}}\) from 0 to 0 is \(\boxed{0}\)