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:
`y_"ave"=(int_a^bf(x)dx)/(b-a`
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?
Question
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.
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