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# Mean Value Theorem for Integrals

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.

## Mean Value Theorem for Integrals

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### Presentation Transcript

1. 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

2. Average Value of a function, f(x) Examples: Find the point(s) on the graph that represents the average value of the function. 1.

3. 2. Find the point(s) on the graph that represents the average value of the function.

4. Function that finds area under curve at any value of x.

5. Second Fundamental Theorem of Calculus (SFTC) If f(x) is continuous on an interval containing x=a, then or 4.

6. 5.

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