In this video I go over an example on using the mean value theorem for integrals to first show that there are 2 x-values that correspond to the average value of the function and then I solve for the x-values.

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Integrals and Average Value: Mean Value Theorem: Example 1

Example 1:

Apply the Mean Value Theorem for Integrals to find which x values the function f(x) = 1 + x² have the average value across the interval [-1, 2].

Solution: