Expert: Ahmed Salami - 1/20/2011

Question
Find the average value of the function on the given interval;
f(x)=e^x/4,[0,9]
the textbook answer is3.772.,but I do not know how to get that answer.Could you show me how step by step. Thanks

Answer
Hi Ken,
In calculus, the average value of a function f(x) in the interval [a,b] is the definite integral of f(x) from a to b divided by (b-a).
Now,
∫e^(x/4) dx = 4e^(x/4)
and the definite integral from 0 to 9 would be
4e^(9/4) - 4e^(0/4)
= 37.95 - 4
= 33.95
The average value is therefore
33.95/(9-0) = 33.95/9
= 3.772

You can read more about average values.

Regards