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AP Calculus AB Chapter 4, Section 4 The Fundamental Theorem of Calculus 2013 - 2014
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The Fundamental Theorem of Calculus
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Evaluate the definite integral
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A definite integral involving Absolute Value
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Using the Fundamental Theorem to Find Area
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Finding the Area of a Region
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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.
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Mean Value Theorem for Integrals
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Using Mean Value Theorem for Integrals
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Average Value of a Function
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Finding the Average Value of a Function
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The Second Fundamental Theorem of Calculus
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Khan Academy Video Integral Calculus https://www.khanacademy.org/math/integral- calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/fundamental-theorem-of-calculus https://www.khanacademy.org/math/integral- calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/fundamental-theorem-of-calculus
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Second Fundamental Theorem of Calculus: Chain Rule
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Khan Academy Video Integral Calculus https://www.khanacademy.org/math/integral- calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/applying-the-fundamental-theorem-of- calculus https://www.khanacademy.org/math/integral- calculus/indefinite-definite-integrals/fundamental-theorem- of-calculus/v/applying-the-fundamental-theorem-of- calculus
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Practice
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Apply Second Fundamental Theorem
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Ch 4.4 Homework Pg. 291 – 292, #’s: 1 – 45 every other odd, 47, 51, 63
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