6.5 Integral Applications
Average Value of a Function
Question #4 (Medium): Proving the Average Value Theorem
Based on the definition of the average value of a function: ∫ , apply a few basic
integral properties to prove any given theorem.
[ ] represents the average value of the function over the interval [ ]. Prove that for any
constant value in the interval, so that , the following relationship holds.
[ ] [ ] [ ]
Rearrange the more complex right side of the given equation: [ ]