Understanding Average Value and the 2nd Fundamental Theorem

Mar 01, 2025

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Learn about the area under the curve between 0 and 2 for a function f(x) and how it relates to rectangles with height y. Explore the Mean Value Theorem for Integrals and why the constant on the bottom doesn't affect the derivative of an integral.

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Understanding Average Value and the 2nd 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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Understanding Average Value and the 2nd Fundamental Theorem

Understanding Average Value and the 2nd Fundamental Theorem

Presentation Transcript

The Fundamental Theorem of Algebra

THE FUNDAMENTAL THEOREM OF CALCULUS

The Mean Value Theorem

The Fundamental Theorem of Arithmetic

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

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

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

The Fundamental Theorem of Calculus

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