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#1 2007-08-21 03:11:30

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

integrating non linear equations

is there any exact way to evaluate the following integral?

ive never integrated anything where the thing to integrate is something that is also changing with time without estimating using a numerical integration method

but is there an exact way to do it?

note, that v_0 is known.

Last edited by luca-deltodesco (2007-08-21 03:14:36)


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#2 2007-08-21 04:08:16

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: integrating non linear equations

Basically, what you are asking to do is to solve:

For all possible functions f(t).  So now that the question is reworded, what is the answer?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2007-08-23 23:38:24

HallsofIvy
Guest

Re: integrating non linear equations

"ive never integrated anything where the thing to integrate is something that is also changing with time without estimating using a numerical integration method"
  ??? Are you saying that you have never integrated, with respect to t, a function of t???  I find that hard to believe. 

  In any case, if you are integrating
v_T = \int_0^T\!\! g - fv_t\  dt = gT - f\!\int_0^T\!\!v_t\ dt
where v_t is some function?  Obviously the result depends on the function!

#4 2007-08-26 10:05:20

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: integrating non linear equations

Can you write out v[sub]t[/sub] explicitly, luca? There might be other ways than computing if you can do so.


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