The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. What is the average value of f over the interval [−2,5] ?

The average value of over the interval is .

Step-by-step explanation:

Let suppose that function is continuous and integrable in the given intervals, by integral definition of average we have that:

(1)

(2)

By Fundamental Theorems of Calculus we expand both expressions:

(1b)

(2b)

We obtain the average value of over the interval by algebraic handling:

The average value of over the interval is .

step-by-step explanation:

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