Problem : Find the average value of f for f (x) = 3x^{2} - 6x on [- 1, 1].
Problem : Find the average value of f for f (x) = sin(x) on [- Π, Π].
Problem : For the function above, find the c on [- Π, Π] such that f (c) = f_{avg}
Problem : Use the second fundamental theorem of calculus to find F'.
F'(x) = 9x + 9
Problem : Now integrate the above expression for F and then take the derivative to find F'(x) and verify the result from the previous question.
This verifies the result given by the second fundamental theorem.