# Thread: Average value of a function

1. ## Average value of a function

What is the basic process of finding the average value for this problem. Find the average value of the function f(x)= sin(x) on the interval [0, pi]

2. You basically solve that integral, and multiply it by 1/(upper bound-lower bound); in this case, it would be 1/Pi.

3. So I'd integrate that function, then multiply by 1/ 1/pi, but where'd you get 1/pi from?

4. Just one over pi. Because that's the definition of average value: 1/(b-a). So you have endpoints 0 and Pi, then the term b-a becomes Pi.

5. Ahh, I see now. Thank you!!

6. Originally Posted by Hibijibi
What is the basic process of finding the average value for this problem. Find the average value of the function f(x)= sin(x) on the interval [0, pi]
Average value of $f(x)$ on $[a,b]$ is $\frac{1}{b-a}\int_a^{b}f(x)dx$

Therefore for $f(x)=\sin(x)$ and $[0,\pi]$ youd have average value is

$\frac{1}{\pi-0}\int_0^{\pi}\sin(x)dx=\frac{1}{\pi}\bigg[-\cos(x)\bigg]\bigg|_0^{\pi}=\frac{2}{\pi}$

7. Ahh, I will def need to remember that for tomorrows exam. Thank you!