Iif your points are (x_0,y_0), (x_1,y_1),...,(x_n,y_n),
don't you just take the sum of the (x_{i+1}-x_i)*(y_{y+1}-y_i)/2 ?
That's a one-liner.
sage: pts = [ (0, 0), (1, 3), (2, 8)]
sage: area = sum([(pts[i+1][0]-pts[i][0])*(pts[i+1][1]-pts[i][1])/2
for i in range(2)])
sage: area
4
On Thu, Apr 9, 2009 at 8:53 AM, hpon <peter.norli...@gmail.com> wrote:
>
>
> Hi,
>
> I'm reading data points from a graph. The points could for example be
> (0, 0), (1, 3), (2, 8). I would like to calculate the integral of the
> piecewise linear segments that these points span.
>
> Ideally, I want a command of this type: integral( (0, 0), (1, 3), (2,
> 8) ). Does such a command exist in Sage?
>
> I found trapezoid_integral_approximation, for instance, but this one
> is messy compared to what I want. Here you need to define the
> interval and local function for each segment, instead of just listing
> the points.
>
> Below is an attempt to use trapezoid_integral_approximation in the
> fashion I desire. It's bulky and does not work.
>
> y_0, s_0, y_1, s_1, y = var('y_0, s_0, y_1, s_1, y');
>
> f (y_0, s_0, y_1, s_1, y)= (y - y_0) * ((s_1 - s_0) / (y_1 - y_0)) +
> s_0;
>
> sigma = Piecewise([[ (0, 1), f (0, 100, 1, 300) ]]);
> print f.trapezoid_integral_approximation(4);
>
> Regards,
> hpon
> >
>
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