Analyzing the Area Under a Curve My goal is to find the area under a curve on a graph that goes from -10 to 10 along the x-axis and from 0 to 100 on the y-axis. The curve will be the result of the line y=x. I will try different methods and improve them to see which one provides the most accurate answer. The graph I am using looks like this: - Square Count Method The first method I will use to find the area is the square count method. For this method I will draw the graph on a cm sheet and estimate the amount of squares occupied by the area under the curve. To do this I will first count all the whole squares, then count all the half squares and divide that number by two to give a rough estimate of the area under the curve. In all I counted 10 whole squares and 14 half squares. When the half squares were divided by 2, the total number of squares was 17 squares. However the number then had to be multiplied by 2 because this would give the amount for both sides of the parabola. This gave me 34 squares. However since each square on my graph represents more than 1cm, instead representing 20cm because it is 2 wide and 10 at the top, I have to multiply my answer by 20 giving me a final answer of 680 squares. However, this answer is only a very rough estimate and there is a high possibility of human error. While counting the half squares I counted every square that the line passed through and this means that it is not very accurate to simply divide the result by 2 because the half squares were not of equal size and simply dividing by 2 would be very inaccurate. Counting Rectangles Next The method I will use should be more accurate than the countingsquares method. I will divide the curve into 5 rectangles and calculate