# Thread: Average value of a function

1. ## Average value of a function

Find the average value fave of the function f on the given interval.

$f(x)=7\sin(10x) , [-\pi, \pi]$

My integral should look like this?

$\frac{1}{\pi-(-\pi)}\int_{-\pi}^\pi \! 7\sin(10x) \, dx$

The bottom bound is supposed to be neg pi

so then we have

$-\frac{7}{20\pi}(\cos(10x))\bigg|_{-\pi}^\pi$

Again...lower bound is neg pi anyone know how i format that when i put a - sign next to the\pi it screws it up. Anyway, am i on the right track here?

2. Originally Posted by mmattson07
Find the average value fave of the function f on the given interval.

$f(x)=7\sin(10x) , [-\pi, \pi]$

My integral should look like this?

$\frac{1}{\pi-(-\pi)}\int_{-\pi}^\pi \! 7\sin(10x) \, dx$

The bottom bound is supposed to be neg pi

so then we have

$-\frac{7}{20\pi}(\cos(10x))\bigg|_{-\pi}^\pi$

Again...lower bound is neg pi anyone know how i format that when i put a - sign next to the\pi it screws it up. Anyway, am i on the right track here?
fixed latex

you're on the right track ...

but note that it's much easier to know the average value of an odd function from $x = -a$ to $x = a$ is zero.

3. Haha wow thanks man i didnt even realize so because its the sign function right