Find an average value

Question

Find the average value of the function over the given interval.
f(x) =8/x^2 , [2, 4]

Answer 1

average value of a function over interval [a,b] = (integral from a to b of f(x))/(b-a)

 

integral 8/x^2 dx from 2 to 4 = integral 8x^-2 dx from 2 to 4 = (8x^-1)/-1 from 2 to 4 = -8/x from 2 to 4 = (-8/4)-(-8/2) = (-2)+(4) = 2

 

average value = 2/(4-2) = 2/2 = 1