AP Calculus AB Chapter 4, Section 4 The Fundamental Theorem of Calculus 2013 - 2014.

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Presentation transcript:

AP Calculus AB Chapter 4, Section 4 The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

Evaluate the definite integral

A definite integral involving Absolute Value

Using the Fundamental Theorem to Find Area

Finding the Area of a Region

Mean Value Theorem for Integrals  The mean value theorem for integrals implies that somewhere in the interval of the integral, there is a point that if you made a rectangle that includes that point, the area of that rectangle would be the area under the curve.

Mean Value Theorem for Integrals

Using Mean Value Theorem for Integrals

Average Value of a Function

Finding the Average Value of a Function

The Second Fundamental Theorem of Calculus

Khan Academy Video  Integral Calculus  calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/fundamental-theorem-of-calculus calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/fundamental-theorem-of-calculus

Second Fundamental Theorem of Calculus: Chain Rule

Khan Academy Video  Integral Calculus  calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/applying-the-fundamental-theorem-of- calculus calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/applying-the-fundamental-theorem-of- calculus

Practice

Apply Second Fundamental Theorem

Ch 4.4 Homework  Pg. 291 – 292, #’s: 1 – 45 every other odd, 47, 51, 63