Re: Integrate f(x(t)) dx/dt dx?
- From: Proginoskes <CCHeckman@xxxxxxxxx>
- Date: Fri, 21 Sep 2007 23:20:12 -0000
On Sep 21, 4:06 pm, Proginoskes <CCHeck...@xxxxxxxxx> wrote:
On Sep 21, 10:52 am, blackhead <larryhar...@xxxxxxxxxxxx> wrote:
f(x(t)) dx/dt dt can easily be integrated using the substitution
method, but how do you integrate f(x(t)) dx/dt dx ? My maths skills
are very rusty, but I get the feeling that a combination of
substitution and integration by parts might work.
It depends on what f(x) and x(t) are.
For instance, if f(x) = e^(-x^2), then there's no hope of integrating.
(You would have to numerically approximate it, use power series, or
some such technique.)
I just saw that you had "dx" in the title of the thread and not "dt".
Since dx = (dx/dt) * dt, then the integral of f(x(t)) dx/dt dx is just
f(x(t)) (dx/dt)^2 dt.
--- Christopher Heckman
.
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