A sin^2 and cos^2 integrals question

[dudinka]

hi!

1. Is the definite integral over [sin(x)]^2 from 0 to a, is a/2? and also the cosine?

2. Is it because the average of the sin/cos functions is always 1/2?

3. and if so, the integration region doesn't matter because the function is positive?
I mean, what about integration from -a to a?

4. and from -3a to 0.5a? is it: 0.5*[3.5a]?

thanks!

 

[dextercioby]

Well, for 1. why do you ask us ? Can't you compute it all by yourself ? The answer is "no", btw. Then you can figure out the aswers to the other questions. And the average of the sin/cos in not always 1/2.

 

[dudinka]

are you trying to help?

I'm asking because I don't know the answers.

 

[dextercioby]

Well, the simple calculation of those 2 integrals doesn't yield the results you proposed. So do you know anything about integral calculus ? I'm asking because the answer will make me post the solutions to those integrals or not...

 

[dudinka]

I've just found a formula on the net for those integrals, thnks anyway.

but I remember my teacher said that integral over squared(!) sin/cos is always 1/2 or something.
Is this correct? if so, for what range?

 

[dextercioby]

Nope, of course not. The range can be let's say for the cos^2 from 0 to the solution of the equation 2a+sin 2a=2.

 

[dudinka]

thanks!