Find the average value of the function
Over the indicated interval .

A) 12
B) 11
C) 13
D) 16

Question

Find the average value of the function ​  ​
Over the indicated interval  .
​
A) 12 
B) 11 
C) 13 
D) 16

Quizplus · Accepted Answer

To find the average value of the function, we need to calculate the definite integral of the function over the given interval, and then divide by the length of the interval.

The definite integral of the function is:

∫(2x+5) dx = x^2 + 5x

Evaluate this from x = 1 to x = 3:

(3^2 + 5(3)) - (1^2 + 5(1)) = 9 + 15 - 1 - 5 = 18

The length of the interval is:

3 - 1 = 2

So the average value of the function is:

18/2 = 9

Therefore, the answer is not given in the choices.

But wait! We made a mistake! We need to divide by the length of the interval last. So, the average value of the function is:

(1/2) * (18/2) = 9

Now, the closest option to the correct answer is C, which is 13. However, the correct answer is 9, so none of the given choices are correct.

Find the Average Value of the Function ​ ​

Find the Average Value of the Function