9. Average Value of a Function
by M. Bourne
The average value of the function y = f(x) from x = a to x = b is given by
Why? When you see a formula like this for the first time, think about where it comes from and why it should work.
Hint: How do we find the average of a set of numbers? What are we really doing each time we find an integral? What does the integral symbol stand for?
Example:
Need Graph Paper?
The temperature T (in °C) recorded during a day followed the curve
T = 0.001t4 − 0.280t2 + 25
where t is the number of hours from noon (-12 ≤ t ≤ 12)
What was the average temperature during the day?
- Answer
-
First, we consider the graph of the situation and estimate that the average should be around 14 to 16 degrees.
What have the following got in common?
- The Average Value of a Function
- The Area under a Curve
- A bag of air
- The most famous car crash in history
- Boxers
All is revealed in Head Injury Criterion.
Find your integral using Mathematica!
Enter multiply using *, square root of x using Sqrt[x] and trigonometry like Sin[x]. See the full list of how to enter math.
Click the blue button to find your integral.
Didn't find what you are looking for on this page? Try search:
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Calculus Lessons on DVD
Easy to understand calculus lessons on DVD. See samples before you commit.
More info: Calculus videos
Book mark this page
Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...
Need a break? Play a math game. Well, they all involve math... No, really!
