Question

Find the average value of the function on the given interval. f(x)=(2x-1)1/2; [1,13]

Answer 1

Answer:

The average value of the function on the given interval 6.5.

Step-by-step explanation:

Consider the given function is

$f(x)=\dfrac{2x-1}{2}$

We need to find the average value of the function on the given interval [1,13].

$f(x)=\dfrac{2x}{2}-\dfrac{1}{2}$

$f(x)=x-0.5$

The average value of the function f(x) on [a,b] is

$Average=\dfrac{1}{b-a}\int\limits^b_a {f(x)} \, dx$

Average value of the function on the given interval [1,13] is

$Average=\dfrac{1}{13-1}\int\limits^{13}_{1} {x-0.5} \, dx$

$Average=\dfrac{1}{12}[\dfrac{x^2}{2}-0.5x]^{13}_{1}$

$Average=\dfrac{1}{12}[\dfrac{(13)^2}{2}-0.5(13)-(\dfrac{(1)^2}{2}-0.5(1))]$

$Average=\dfrac{1}{12}[78-0]$

$Average=6.5$

Therefore, the average value of the function on the given interval 6.5.