Answer:
The average value of the function on the given interval 6.5.
Step-by-step explanation:
Consider the given function is
[tex]f(x)=\dfrac{2x-1}{2}[/tex]
We need to find the average value of the function on the given interval [1,13].
[tex]f(x)=\dfrac{2x}{2}-\dfrac{1}{2}[/tex]
[tex]f(x)=x-0.5[/tex]
The average value of the function f(x) on [a,b] is
[tex]Average=\dfrac{1}{b-a}\int\limits^b_a {f(x)} \, dx[/tex]
Average value of the function on the given interval [1,13] is
[tex]Average=\dfrac{1}{13-1}\int\limits^{13}_{1} {x-0.5} \, dx[/tex]
[tex]Average=\dfrac{1}{12}[\dfrac{x^2}{2}-0.5x]^{13}_{1}[/tex]
[tex]Average=\dfrac{1}{12}[\dfrac{(13)^2}{2}-0.5(13)-(\dfrac{(1)^2}{2}-0.5(1))][/tex]
[tex]Average=\dfrac{1}{12}[78-0][/tex]
[tex]Average=6.5[/tex]
Therefore, the average value of the function on the given interval 6.5.
