Thanks for the reply. Ok, yeah, it's just that it wasn't written as ln in the equation, so one would assume it's ##log_{10}##. I have always known log with no subscript to mean ##log_{10}## (because it's the most common), not sure about other people.
Thanks, is that a log(base 10) in ##e^{i(x\log 2)}##? I understand the algebra you mention although I'm trying to gain an understanding of how best to understand imaginary space, particularly its application to wavefunctions expressed in exponential form. One thing I find very strange is that...
I'm trying to get a more intuitive understanding of Euler's identity, more specifically, what raising e to the power of i means and why additionally raising by an angle in radians rotates the real value into the imaginary plane. I understand you can derive Euler's formula from the cosx, sinx and...
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Let's say you have a laser cavity with two mirrors at either end, one is considered 100% reflective, the other 99.9%, so that a wave beam is emitted through this lower reflectivity mirror.
I know...
Yeah, that makes sense. Do you know of any way in which you can calculate the total area under a sine function without breaking down the limits or does the question itself not make sense? Integrating something akin to a rectified sine wave? $$|sin(x)|$$
So squaring the function will rectify it and then the subsequent values calculated in the integral of interval a->b then rooted will be the same as:
$$\int_a^b |sin(x)|\,dx$$
Is that correct?
So I just calculated it myself and they are not equivalent.
$$\int_a^b |sin(x)|\,dx \neq...
I understand that if you have a function in which you want to determine the full (i.e. account for positive and negative values) integral you need to break down your limits into separate intervals accordingly.
Is there any way in which you can avoid this or is it mathematically impossible? If...