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Mean Value Theorem for Integrals. If f(x) is continuous on [a, b], then there exists a number x=c in [a, b] such that. For continuous functions, there must be some average value such that the area under the original curve is equal to the average value multiplied by the length from x=a to x=b.

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## Mean Value Theorem for Integrals

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**Mean Value Theorem for Integrals**If f(x) is continuous on [a, b], then there exists a number x=c in [a, b] such that For continuous functions, there must be some average value such that the area under the original curve is equal to the average value multiplied by the length from x=a to x=b. f(c) a c b**Average Value of a function, f(x)**Examples: Find the point(s) on the graph that represents the average value of the function. 1.**2.**Find the point(s) on the graph that represents the average value of the function.**Second Fundamental Theorem of Calculus (SFTC)**If f(x) is continuous on an interval containing x=a, then or 4.

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