Average Value and the 2 nd Fundamental Theorem. What is the area under the curve between 0 and 2? f(x)

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Presentation transcript:

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)

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

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

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).