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Ch 4.4 – The Fundamental Theorem of Calculus (day 2)

Ch 4.4 – The Fundamental Theorem of Calculus (day 2). Target Goals: Find the value of c guaranteed by the Mean Value Theorem for Integrals Find the average value of the function over an interval. Mean Value Theorem for Integrals.

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Ch 4.4 – The Fundamental Theorem of Calculus (day 2)

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  1. Ch 4.4 – The Fundamental Theorem of Calculus (day 2) Target Goals: Find the value of c guaranteed by the Mean Value Theorem for Integrals Find the average value of the function over an interval.

  2. Mean Value Theorem for Integrals • If f is continuous on [a, b], then there exists a number c in the interval [a, b] such that:

  3. Average Value of a Function • The value of f (c) given by the MVT for integrals is the average value of f on [a, b]. • If f is integrable on [a, b], then the average value of f on the interval is:

  4. Example 1 • Find the value of c guaranteed by the MVT for integrals:

  5. Visual Representation of Average Value of a Function and MVT • http://archives.math.utk.edu/visual.calculus/5/average.1/ • The area of the region under the graph of f is equal to the area of the rectangle whose height is the average value.

  6. Example 2 • Find the average value and all values of x in the interval for which the function equals its average value. Average value

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