MATH 1231 Lecture 24: Region Area Estimate by Counting
10 Nov 2015
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Math 1231 lecture 24 region area estimate by counting. Area of a rectangle is length x breadth. If we consider it to be in general it is x2. So we have a kind of triangle but the diagonal is not straight and it"s curved. Also we notice that the sum of the areas of all the rectangles is greater than the triangle. We notice that now the sum of the rectangle areas is closer to the area of the triangle when considering more points but lesser intervals. Similarly, we can estimate the area: note that we have to pick every small interval from the right point. Let"s see what happens if we pick from the left point. Notice that the sum of all the areas of the rectangle is lesser than the area of the triangle. So we should follow one technique: either pick right or left point and find the estimate.
