Question

Find the average value of the function over [1,3] and all values of x in the interval for which the function:

f(x)= 4(x^2+1)/x^2 equals its average value.

Answer 1

do the integral 4(x^2+1) dx/x^2and divide by the span which is 3-1 = 2

4 x^2 dx/x^2 + 4 dx/x^2
is
4 x - 4/x = 4 (x-1/x)
at 3 = 4(3-1/3) = 32/3
at 1 = 0
so 32/3
divide by 2
16/3