Final Answer:
The correct option is a) ∫f(x)dx / (b - a).
Step-by-step explanation:
The average value of a function f(x) over the interval [a, b] is given by the formula 1 / (b - a) ∫[a]^[b] f(x) dx. This is represented by option a) ∫f(x)dx / (b - a). The integral ∫[a]^[b] f(x) dx calculates the total area under the curve of f(x) over the interval [a, b], and dividing it by the width of the interval (b - a) gives the average value.
Options b) and c) have incorrect denominators, and option d) "None of the above" is not accurate, as option a) represents the correct formula for the average value of a function over an interval.
Understanding the concept of average value is crucial in calculus, and it is essentially the height of a rectangle with the same area as the region under the curve. The provided formula ensures that the average value is appropriately calculated by considering both the function values and the interval width. Therefore, option a) is the correct choice for finding the average value of f(x) over the interval [a, b].