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My favourite field-improvised planimeter consists of (a) tracing out the figures and cutting them out of paper, then (b) weighing the paper shapes with an analytical balance and dividing out by the weight of a unit area's worth of paper.

[emmelaich]

Not surprisingly, this technique is used for numerical integration of complex graphs.

[mensetmanusman]

My advisor’s thesis had an entire section on that for computing complex integrals.

[lupire]

That's Galileo's method of integration.