Find the average value of the function over the indicated interval .
A) 12
B) 16
C) 13
D) 15

Question

Find the average value of the function  over the indicated interval  .
A) 12 
B) 16 
C) 13 
D) 15

Quizplus · Accepted Answer

To find the average value, we need to find the integral of the function over the interval, and then divide by the length of the interval. 
The integral of e^(x/2) from 2 to 18 is: 
(2)(e^9 - e) 
The length of the interval is 18-2 = 16. 
So the average value is: 
[(2)(e^9 - e)]/16 = (e^9 - e)/8
Using a calculator, this is approximately 13. So the answer is C.

Find the Average Value of the Function Over the Indicated