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Integration

Started by Theriomorph Mar 31, 2004 at 6:38 AM 10 replies 800+ views

Original Post

Mar 31, 2004 at 6:38 AM

I don''t remember some of the terms from calculus but i''ve been reading alot of things mentioning integration lately (i''ve been looking into springs) and I was wondering if this is the same thing or is it something different? ie. 3x^2 integrated becomes x^3 (if thats the right one

)

Nervo

Mar 31, 2004 at 6:42 AM

yes thats correct. To be more precise its really x³ + C where c is a constant. c can also be zero, making it just plain x cubed.

Theriomorph

Mar 31, 2004 at 6:51 AM

I remember losing marks for forgetting that on more than one occasion

So whats the difference between Euler Integration and some others (Sorry, I can't remember their names...)?

[edited by - Theriomorph on March 31, 2004 7:53:54 AM]

szinkopa

Mar 31, 2004 at 8:20 AM

Check out the the 8th post in the "car engine simulation" thread, I wrote it.

oliii

Mar 31, 2004 at 4:45 PM

there are lots of things that depends on the method for integration. Stability, accuracy, timesteps size and variability, aliasing effects, simplicity, conservation of enery, convergence, ect...

popular examples : euler, RK4, verlet, leapfrog, combinations of them, and many more... I remember reading a pretty thourough comparision (pros and cons) of the different integration algorithm in the Game Physics book br D.Eberly, there were about 6 or 7 of them.

I''m not a maths specialist, but they are more of less derived from a taylor expansion series, to different degrees. Verlet, for example uses positions and accelerations to calculate the next position. The velocity is ''implicit'', it''s derived from the integration, not used in the integration itself to calculate the next position. It''s apparently good at conserving kinetic energy, and is apparently used in molecular dynamics a lot. However, Verlet is not very good with variable timesteps (from my experience).

Promit

Mar 31, 2004 at 4:46 PM

quote:
Original post by Theriomorph
I remember losing marks for forgetting that on more than one occasion

If you''re doing physics work instead of pure math, you simply cheat by integrating from 0 to x

oliii

Mar 31, 2004 at 5:17 PM

Agony

Mar 31, 2004 at 5:27 PM

Integration Methods usually refers to methods of approximating integrals that have no closed solution. Obviously, if you want to calculate the integral of 3x^2, you just calculate x^3. However, many integrals can''t be solved precisely like that, so approximations are needed.

Doc

Mar 31, 2004 at 11:14 PM

How the hell did you manage to double post half an hour apart?

Doc

Mar 31, 2004 at 11:16 PM

quote:
Original post by Agony
[However, many integrals can''t be solved precisely like that, so approximations are needed.

e^(-(x^2))

O_o

Mar 31, 2004 at 11:26 PM

You can integrate anything you just can''t always get a closed form solution =p

Pragma

Apr 1, 2004 at 2:35 AM

Actually, you can''t integrate *anything*. A very interesting result from measure theory says that there are some functions which are not even Lebesgue measurable. This means you cannot assign any value to their integrals without resulting in a contradiction.
/Total Math Dork

"Math is hard" -Barbie

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