Find the average value of f(x)=e^2x over the interval [2, 4].

Question

Find the average value of f(x)=e^2x over the interval [2, 4].

1463.18

731.59 

1517.78 

23.60

Answer 1

The average of a function over an interval is computed as (1/width of interval) times the definite integral of the function evaluated over the interval. The indefinite integral of e^2x is (1/2)e^2x. So the answer is found by evaluating:

(1/2)*[(1/2)[e^8 - e^4]], or (1/4)[e^8 - e^4]

which equals about 731.6.