Step 1 :The integral represents the area under the curve of the function \(f(x) = \sqrt{3^{2}-x^{2}}\) from \(x = -3\) to \(x = 3\). This function describes a semi-circle with radius 3.
Step 2 :The area of a semi-circle is given by the formula \(\frac{1}{2} \pi r^{2}\), where \(r\) is the radius of the circle. In this case, \(r = 3\).
Step 3 :Substituting \(r = 3\) into the formula, we get the area as approximately 14.14 square units.
Step 4 :This is the value of the integral.
Step 5 :Final Answer: The value of the integral is approximately \(\boxed{14.14}\).