Calculating the Average Value of a Function over an Interval | Formula and Steps

Average Value (c) found by…

To find the average value (c) of a function over a given interval, we can use the following formula:

c = (1 / (b – a)) * ∫[a to b] f(x) dx

In this formula, “a” represents the lower limit of the interval, “b” represents the upper limit of the interval, f(x) represents the function, and ∫[a to b] denotes the definite integral of the function over the interval [a, b]

To find the average value (c) of a function over a given interval, we can use the following formula:

c = (1 / (b – a)) * ∫[a to b] f(x) dx

In this formula, “a” represents the lower limit of the interval, “b” represents the upper limit of the interval, f(x) represents the function, and ∫[a to b] denotes the definite integral of the function over the interval [a, b].

To compute the average value, we follow these steps:

1. Determine the function f(x) for which you want to find the average value.
2. Identify the interval [a, b] over which you want to evaluate the average value.
3. Evaluate the definite integral ∫[a to b] f(x) dx.
4. Calculate (1 / (b – a)).
5. Multiply (1 / (b – a)) by the definite integral to obtain the average value (c).

The average value (c) is a representative value of the function over the given interval. It can be thought of as the value that the function would need to maintain over the entire interval to have the same total area (or cumulative effect) as the actual function over that interval.

Note that the average value can be interpreted as a sort of “mean” value of the function over the given interval, but it does not necessarily coincide with any specific value that the function takes within the interval.

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