Problem

Find the average value of the function on the given interval. \[ f(x)=x^{2}-5 ;[0,3] \] The average value is (Type an integer or a fraction.)

Solution

Step 1 :The average value of a function on the interval [a, b] is given by the formula: \[\frac{1}{b-a} \int_{a}^{b} f(x) dx\]

Step 2 :In this case, we need to find the average value of the function f(x) = x^2 - 5 on the interval [0, 3].

Step 3 :So, we need to calculate the integral of the function from 0 to 3, and then divide it by the length of the interval, which is 3 - 0 = 3.

Step 4 :The average value of the function f(x) = x^2 - 5 on the interval [0, 3] is -2. This is the result of the integral calculation and the division by the length of the interval.

Step 5 :Final Answer: \(\boxed{-2}\)

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Source: https://solvelyapp.com/problems/AlbwZ7ko7u/

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