Seemingly impossible
Set A contains all the possible numbers from 0 to 3 i.e (0.1,0.001,2,2.001....)
Set B contains all these elements after they go through the function f(x)=x^2
What is the average of all the elements in set B?
Note: the number if elements is infinite.
The answer is 3.
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1 solution
The answer is integrating the function with the limits 0 to 3/3=3 This question sort of defines what integration is fundamentally, to visualize imagine taking every number in the set A and putting it through f. If for every input you mark the output you will pretty much end up drawing the function. The average value of the set B is equal to the average height of the curve. As dividing by an infinitely large number is the same as multiplying by an infinitesimally small number...... in other words dx.