/sci/ - Science & Math

But if you integrate (to get the surface area of sinx/x in the (x,y) plane)
The negative stuff becomes negative surface in the integration, I believe
http://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Integral_example.svg/220px-Integral_example
.svg.png
So it's automatically going to be a negative volume after rotation
No ?

>>3524756
Yeah nevermind I think I went full retard

erm, won't that work out to be zero seeing as the graph is symetrical about the Y axis? you will have as much positive volume as negative volume so they will cancel out.

homoeeewoorrrkkkk
ololololololooooo

( look how I put homo into homework, OP is a FAG )

Use polar coordinates.

>>3524781

I meant negative in the y coordinates, not the x coordinates. Sorry for leaving that all ambiguous though.

>>3524783

It's not homework, it's personal study, if that makes it any better. I'm trying to write a proof on probability waves but am at a complete stand-still here.

integrate
phi from 0 to your_angle_of_rotation
rho from x0 to x1
sin(rho)/rho

=

integrate
phi from 0 to your_angle
Si(x1) - Si(x0)

=

your_angle * (Si(x1) - Si(x0))

with
x0 lowerbound, x1 upperbound of interval
Si = http://mathworld.wolfram.com/SineIntegral.html

disclaimer, I suck at maths

>>3524801
ah i see. what range of x-values will you be doing this for? like to infinity in both directions?
If you are doing it for a finite range then you can simply do it the slow way and do your integrations between the x intercepts each time, and then just by observation you can add a positive or negative prefix onto them.

if to infinity, then i have no idea how you would go about doing it...

>>3524801
I think it would suffice to stay in the interval [-pi,pi]

Leads to ∫ sin x dx. That one does not converge, although it does give a clue that the answer is in some sense 0.

>>3524809

Thanks, but this is exactly what i attempted.

Doing that yields 2*pi*x*(sin(x)/x), which is (2*pi*sin(x)). Now, that would mean that there is an infinite volume (since there are no limits at infinity for sin(x) ), which i guess would make sense, but i can't help thinking there being something wrong with that.

>>3524823

Well, its ( Si(x) ) limits at infinity and -infinity are pi/2 and -pi/2 respectively, so the traditional sin(x) / x function in 2-D has an area "under the curve" of pi. That's what gives me hope that the volume of it's 3-D version should also be finite.

> However, i need the areas that are negative in the 2-D plot to count as "negative" volume when calculating the total volume

This is a non-issue; it will happen anyhow. If you wanted them to count as /positive/ volume, then you'd have an issue.

Other than that, see:

http://en.wikipedia.org/wiki/Multiple_integral#Polar_coordinates

>>3524810

Yeah, it's toward both infinities. Who would have thought attempting to come up with a unitary 3-D probability wave that diminishes proportional to its distance would have been so tough?

>>3524853

This seems like a genuinely good suggestion, thanks! I'm no math whiz so i know dicksquat about this kind of transformation, but i'll certainly read up and give it a go.

>>3524855
I think you need a function that decays faster e.g.
(sinx/x)^2 or (sinx/x)^3