6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4.

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Presentation transcript:

6/3/2016 Perkins AP Calculus AB Day 10 Section 4.4

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

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

Using the 2 nd Fundamental Theorem of Calculus:

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.

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

Perkins AP Calculus AB Day 10 Section 4.4

The Mean Value Theorem for Integrals

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

Second Fundamental Theorem of Calculus