Question

Find the average value of the function on the given interval.

f(x)= √x+2; [1,7]

Answer 1

did you mean it the way you typed it, or did you mean
f(x) = √(x+2) ?

I will assume f(x) = √(x + 2) judging by the values of the interval

first take the definite integral of the function

= ∫(x+2)^(1/2) dx from 1 to 7
= (2/3)(x+2)^(3/2) | from 1 to 7
= (2/3)9^(3/2) - (2/3)(3^(3/2))
= (2/3)(27) - (2/3)(3√3)
= 18 - 2√3

Average value
= definite integral/domain
= (18-2√3)/(7-1)
= 3 - √3/3

check my arithmetic
If you meant your function the way you typed it, follow the same procedure, it does not come out that "nicely".
=

Answer 2

Perfect!!!