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Average Value of a Function and the Second Fundamental Theorem of Calculus

Learn to find the average value of a function on a given interval and locate where it is attained, utilizing the Second Fundamental Theorem of Calculus.

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Average Value of a Function and the Second Fundamental Theorem of Calculus

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  1. AP Calculus AB Day 10 Section 4.4 Perkins

  2. The Mean Value Theorem for Integrals Gives the average value of f(x) on [a,b].

  3. 1. Find the average value of on [1,4]. Then find where f(x) obtains this average value. This value is obtained when…

  4. Using the 2nd Fundamental Theorem of Calculus:

  5. Second Fundamental Theorem of Calculus In order to use this shortcut we must have… a derivative… of an integral… whose lower bound is constant… and whose upper bound is a function of x.

  6. We don’t know how to integrate this function! Using the 2nd Fundamental Theorem of Calculus:

  7. AP Calculus AB Day 10 Section 4.4 Perkins

  8. The Mean Value Theorem for Integrals

  9. 1. Find the average value of on [1,4]. Then find where f(x) obtains this average value.

  10. Second Fundamental Theorem of Calculus

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