Final answer:
The average value of the function f(x) = sqrt(x + 2) over the interval [1, 7] is 5.04.
Step-by-step explanation:
To find the average value of a function on a given interval, you need to find the definite integral of the function over that interval and divide it by the length of the interval.
In this case, the function is f(x) = sqrt(x + 2) and the interval is [1, 7].
The definite integral of f(x) from 1 to 7 is (2/3)(x + 2)^(3/2) evaluated from 1 to 7, which equals (2/3)(7 + 2)^(3/2) - (2/3)(1 + 2)^(3/2) = 30.66 - 0.4 = 30.26.
The length of the interval [1, 7] is 7 - 1 = 6.
Therefore, the average value of f(x) over the interval [1, 7] is 30.26/6 = 5.04.
Complete question
Find the average value of the function on the given interval. Round the answer to two decimal places if necessary. f(x)= sqrt(X+2); [1, 7] O A. 2.69 B. 3.63 OC. 2.08 OD. 2.42