Average Value of a Function - Concept

Concept Concept (1)

Calculating the average value of a function over a interval requires using the definite integral. The exact calculation is the definite integral divided by the width of the interval. This calculates the average height of a rectangle which would cover the exact area as under the curve, which is the same as the average value of a function.

Sample Sample Problems (3)

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Average Value of a Function - Problem 1
Problem 1
How to find the average value of a function, f = root(x), over an interval [a,b] with definite integrals.
Average Value of a Function - Problem 2
Problem 2
How to use definite integrals to find the average value of a function, f= 12x/(x^2 + 16), over an interval [a,b].
Average Value of a Function - Problem 3
Problem 3
How to find the average value of a function, f = x^(2/3) * (8-x), over an interval by finding the definite integral and dividing it by the length of the interval.