# Thread: Value of sin x for different intervals

1. ## Value of sin x for different intervals

I have been asked what the average value of the sin x for the interval greater or equal to 0 and less than or equal to 2 pi. I just plugged in the two end values and since both are = 0 the answer is, of course, 0.

Then I was asked what the average value of this is between 0 and pi

Obviously I am doing something wrong because the answer is 2/pi!!! Please advise on how to do these correctly. Thank you very much

2. You are right actually!

The average is 2/pi. Why do you think it is wrong?

3. Average value of a function f(x) in the interval between a and b is
$\frac{\int^{b}_{a}f(x)~dx}{b-a}$

4. ## value of sin x

So, if I have this right it goes like this:

it would be the value of -cos x from 0 to pi divided by pi - 0

-cos pi + -cos 0 /pi = 1+1 / pi or 2/pi Is this correct figuring? Thanks so much for helping out quickly!

5. Originally Posted by Frostking
So, if I have this right it goes like this:

it would be the value of -cos x from 0 to pi divided by pi - 0

-cos pi + -cos 0 /pi = 1+1 / pi or 2/pi Is this correct figuring? Thanks so much for helping out quickly!
Yes