TI-M: Re: Yet another integral question...
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TI-M: Re: Yet another integral question...
Don't know if there is a way to find the exact integral. But I do know how
to get a good numeric approximation.
Use the list editor to create these three lists:
T = the sequence {2, 1.9, 1.8, 1.7...0.1, 0}
X = X1T(T)
Y = Y1T(T)
This will create a list of (X, Y) points. Use the numerical integeration
method of your choice to estimate the integral. Or, use you calc's
regression capabilities to find a function (Y1) that approximates Y(X) and
calculate fnInt(Y1,X,5*sin(2),10).
The answer is somewhere around 0.582.
----- Original Message -----
From: <JayEll64@aol.com>
To: <ti-math@lists.ticalc.org>
Sent: Monday, October 2, 2000 21:06
Subject: TI-M: Yet another integral question...
>
> Let's say I have two parametric functions x(t) and y(t). How do I find
the
> definite integral of y(x) dx between two bounds, given that y(x) is itself
a
> function but one I'm unable to define explicitly? I'm trying to find the
> area between the curve define by...
>
> x(t) = 5*(sin(t) - (t - 2)*cos(t))
> y(t) = -5 * (cos(t) + (t - 2)*sin(t) - 1)
>
> ...and the x-axis, from t = 2 to t = 0 [ x = 5*sin(2) to x = 10 ]. As far
as
> I know, you can't express y in terms of x alone, even though it is a
function
> of x on the given interval (well...at least I think so...). Any ideas to
do
> this without approximating? And if I had to approximate...what would be
the
> best (easiest?) method to approximate it?
>
> Thanks, just keeping this list alive :)
>
> JayEll
>
>
References: