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After brief review of the "141" quadratic ru. There are many others tutorials which go through trapezoidal rule in a very difficult way. This tutorial is by far the simplest method of explaining it which.
Area of irregular polygon. Is a simple but powerful method for approximating signed area via "quadratic approximations". #01 numerical integration | method to find area of irregular faces.
This video shows how you can find the area of a polygon using grid lines it is shown upon pick's theorem.