Try these solved problems on your own. You know the drill.
PROBLEM 1. Find the average value of f(x) = on the interval [1, 3].
Answer: According to the Mean Value Theorem, the average value is found by evaluating
Your result should be
PROBLEM 2. Find the average value of f(x) = sin x on the interval [−π, π].
Answer: According to the Mean Value Theorem, the average value is found by evaluating
Integrating, we get
(−cos x) = (−cos π + cos(−π)) = 0PROBLEM 3. Find .
Answer: According to the Second Fundamental Theorem of Calculus,
PROBLEM 4. Find .
Answer: According to the Second Fundamental Theorem of Calculus,