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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)
The Beginning Of All Things To End.
The End Of All Things To Come.
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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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"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!
Can you write out v[sub]t[/sub] explicitly, luca? There might be other ways than computing if you can do so.
X'(y-Xβ)=0
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