Mean-Value Theorem for Integrals

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Presentation transcript:

Mean-Value Theorem for Integrals AP Calculus Ms. Olifer

Mean Value for Integrals b c If f(x) is continuous on the closed interval [a, b], then there exists a number c in the closed interval [a, b] such that

Mean Value for Integrals Since We can solve for The theorem does not give us the value of c How can we find it?

Given f(x) = x2 + 4x + 1 on [0,2]. Find the value of c so that

Average value of a function The average value of function f on the interval [a, b] is defined as Example: Find the average value of f(x)=x3 on [0,2].

Example Find the average value of on the interval [0.5, 2]