In this video I go over another video on the average value of a function and derive the formula for average value using integrals. This is important when averaging out an infinite amount of numbers as opposed to simple finite amount of numbers which require adding them up and dividing by the total amount of numbers.

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Integrals and Average Value

It is easy to calculate the average value of a finite amount of numbers:

But how do we compute the average temperature during a day if infinitely many temperatures are possible?

To calculate this we once again use the concept of breaking the function into many parts and summing to infinity and writing as an integral.

For a positive function, we can think of this as saying:

Area/Width = Average Height