Help, I'm a mathlet who doesn't understand how are

bumping for interest

>>371005
I don't think this is true. We know the cosine part doesn't change if x changes to -x, so you can actually simplify this to

d*x*sin(d*x) = d*|x|*sin(d*|x|) - 1

where d = pi*n. Well it turns out that without the -1, these equations are actually equal, because at points where sin would be negative on either side, it gets canceled out. Not sure how to explain it best, but if you plug in something like dx = -.5pi and dx = 1.5pi you'll see that it's right. But the -1 fucks everything up and makes the equation permanently imbalanced.

File: graph.png (103KB, 1917x618px) Image search: [Google]

103KB, 1917x618px

>>371086
I graphed it just to make sure, with n=3 - like I expected, if you change that 1 to a 0 they are exactly equal. Unless I am misunderstanding that equals sign, the equality is invalid.

>>371086
>>371111
As you said,

cos(dx) = cos(-dx) = cos(d|x|)

dx sin(dx) = d|x| sin(d|x|) if x >= 0
dx sin(dx) = -d|x| sin(-d|x|) = -d|x| (-sin (d|x|)) = d|x| sin (d|x|) if x < 0

So the terms are equal except the -1. You can still argument that you get a different constant C' instead of C if n is constant and x>= 0, for example.

>>371126
And? You can call the equations parallel or something, but not equal.

Probably should have specified that this was actually a part of a larger problem https://www.integral-calculator.com/#expr=%7Cx%7Ccos%28n%2Api%2Ax%29&lbound=-1&ubound=1&simplify=1 .
While trying to get the definite integral I noticed that the -1 just sort of appears. Anyone knows how and why?

>>371161
So your actual question is
>how did 2 different methods come up with a different, but pseudo-similar expression

>>371005
>Ignore the constant, it's irrelevant.
No it's not. The C in the first expression is not equal to the C in the second expression.
The difference is that constant term 1/pi^2n^2.

(When computing antiderivatives, you can just add an arbitrary constant.)