• Definite Integral
• Theorem I
• Theorem II
• Average F. V.
• Area I
• Area II
• Volume

If a function is continuous on a closed interval [a, b], there exists a point, c, inside the interval such that:

Examples

1. Find the value of c, the average function value, of the function f(x) = 3x² on the interval [−4, −1].

Since the function is continuous on the interval [−4, −1], the average function value can be applied.

The positive solution is not valid because it does not belong to the interval.

2. Is the average function value applicable to the following function in the interval [0, 1]?

Since the function is continuous on the interval [0, 1], the average function value is applicable and can be applied.

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