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Average Value and the 2 nd Fundamental Theorem

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What is the area under the curve between 0 and 2? f(x)

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Is there a rectangle of length 2, height y where 2y = f(x) from 0 to 2 f(x)

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Is there a rectangle of length 2, height y where 2y = f(x) from 0 to 2 f(x)

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Is there a rectangle of length 2, height y where 2y = f(x) from 0 to 2 f(x)

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a b Mean Value Theorem for Integrals or average value of a function

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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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5.3 Definite Integrals. Example: Find the area under the curve from x = 1 to x = 2. The best we can do as of now is approximate with rectangles.

5.3 Definite Integrals. Example: Find the area under the curve from x = 1 to x = 2. The best we can do as of now is approximate with rectangles.

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