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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