I'm writting a paper about tratidional (historical) methods of finding the area of figures (highschool level - second year of IB programme, actually). I want to show some of the easier methods.
My problem is - in articles about numerical integration (which is, if I understand correctly, a way of finding an area under the curve with a certain accuracy), but my teacher told me about "method of exhaustion". I looked up some articles about this method, but I'm not sure - is it a method of numerical integration? Can I say that those are the same in my paper? What actually is the method of exhaustion? The articles I found are not very clear about how this method works. Is is the same as trapeizodal rule, or "method of rectangles"?
My problem is that english is not my first language, so this is probably why I don't get those articles. So if someone could explain the differences in all of those methods, but not with very complicated vocabulary - I would be very thankful.