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. for example, from -3a to 0.5a? is it: 0.5*[3.5a]?