Integral Calculus

Step 1: Formula for the average value of a function.
The average value of a function on the interval is given by the formula:

Step 2: Applying the formula to the given function.
For on , the average value is:

Step 3: Recognizing the integral.
The integral is the area of a semicircle with radius 3, which is:

Step 4: Calculating the average value.
Substituting this into the formula for the average value:

Step 5: Conclusion.
The average value of the function is .