Let a < b < c and f an integrable function defined on ſa, c). Let the average value of f over [a, b] be A1 and the average value of f over [b, c] be A2. What is the average value of f over [a, c] in terms of the a, b,c, A1, and A2?

By definition of average values, we have

And similarly, we have

The number we're looking for, i.e. the average value of over , is

Using the linearity of the integral, we have

And substituting from the first two equations we have

the answer is d

hope this

-1/4 > -1 2/3. -1/4 is greater than -1 2/3 because it is closer to 0 on the number line.