Average Value and the 2 nd Fundamental Theorem

Mar 21, 2019

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Average Value and the 2 nd Fundamental Theorem. What is the area under the curve between 0 and 2?. f(x). Is there a rectangle of length 2, height y where 2y =  f(x) from 0 to 2. f(x). Is there a rectangle of length 2, height y where 2y =  f(x) from 0 to 2. f(x).

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Average Value and the 2 nd Fundamental Theorem

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Average Value and the 2nd Fundamental Theorem
What is the area under the curve between 0 and 2? f(x)
Is there a rectangle of length 2, height y where 2y =  f(x) from 0 to 2 f(x)
Is there a rectangle of length 2, height y where 2y =  f(x) from 0 to 2 f(x)
Is there a rectangle of length 2, height y where 2y =  f(x) from 0 to 2 f(x)
Mean Value Theorem for Integrals or average value of a function b a

What this says that the constant on the bottom doesn’t matter when we take the derivative of an integral. The derivative of the integral is the original integrand (but with the variable changed).

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Average Value and the 2 nd Fundamental Theorem

Average Value and the 2 nd Fundamental Theorem

Presentation Transcript

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The Mean Value Theorem

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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

Fundamental Theorem

Rolle’s Theorem and the Mean Value Theorem

The Mean Value Theorem and Rolle’s Theorem

2. Rolle’s Theorem and Mean Value Theorem

Section 2: Rolle’s Theorem &amp; The Mean Value Theorem

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

4.4 2 nd Fundamental Theorem of Calculus

Rolle’s Theorem and The Mean Value Theorem

The Fundamental Theorem of Calculus

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Section 5.5 The Intermediate Value Theorem Rolle’s Theorem The Mean Value Theorem

Rolle’s Theorem and the Mean Value Theorem

3.2 Rolle’s Theorem and the Mean Value Theorem

THE FUNDAMENTAL THEOREM OF CALCULUS

The Fundamental Theorem of Calculus

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Section 2: Rolle’s Theorem & The Mean Value Theorem