Investigating The Area Under A Curve
My aim 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 attempt several methods and
improve on them to see which one gives the most accurate answer. The
graph I am using looks like this: -
Counting Squares Method
The first method I will use to find the area is the counting squares
method. For this method I will draw the graph on cm paper and estimate
the amount of squares that the area under the curve takes up. To do
this I will first count all the whole squares, and then count all the
half squares and divide that number by two to give a rough estimate of
the area under the curve.
Altogether 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 as each square on my graph represents more than
1cm, instead it represents 20cm because it is 2 wide and 10 up, I have
to multiply my answer by 20 giving me a final answer of 680 squares.
This answer however is only a very rough estimate and there is a high
possibility of human error. When I was counting the half squares I
counted every square that the line passed through and this means that
it is not very accurate to just divide the answer by 2 because the
half squares were not equal sizes and to just divide by 2 would be
very inaccurate.
Counting Rectangles
The next method I will use should be more accurate than the counting
squares method. I will split the curve into 5 rectangles and calculate
The X- intercept is (0,0) (0, 8.3) and the Y-intercept is (0,0). This shows that the horizontal range is 8.3.
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