Final answer:
To find the average value of the expression over the given interval, calculate the definite integral and divide by the length of the interval.
Step-by-step explanation:
To find the average value of (x²-1)^(1/2) / x for the range 1 ≤ x ≤ 9, we need to calculate the definite integral of the given expression over the specified interval and then divide it by the length of the interval.
Step 1: Calculate the integral of (x²-1)^(1/2) / x with respect to x.
Step 2: Evaluate the integral at the upper limit (9) and subtract the value of the integral at the lower limit (1).
Step 3: Divide the obtained value by the length of the interval (9-1 = 8) to find the average value.
By following these steps and performing the necessary calculations, you can find the average value of the given expression.