Excel has made advanced mathematics possible for everyone to enjoy, you just need the right formula. Excel has proven to be an invaluable tool to professionals from all disciplines allowing massive amounts of data to be easily analysed and translated in to chart and graph form. Calculating the area under a curve known as the definitive integral is one of the basic tools of calculus and is used primarily in the fields of science and engineering. An example of how calculating the area under a curve can be used in real life would be calculating the volume of water in a swimming pool with a gradual curved decline in the depth of the pool.
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Prepare your graph with the data in a table showing X values in column A and Y values in column B.
Enter the following calculation into column C of the table alongside your first line of values for X and Y “= (B2+B1) / 2 * (A2-A1)” where B2 is the value in the second line of data and B1 is the value in the first line of data in the Y column, the same applies to the data for A1 and A2 for the X axis values.
Copy the formula you have just calculated downwards to calculate the rest of the values by selecting the box and either copying and pasting into each subsequent box below, or dragging the formula downwards by clicking on the bottom right hand corner of the cell.
Enter the formula “=SUM (C1:C10)” under your list of calculations in the C column where C1 is the first figure and C10 the last figure you calculated (if you have more than 10 rows of data you would enter C then the row number of the last row in your table). This will give you the area under the curve using the trapezoid rule.
Enter the following calculation into column D of the table, alongside your first line of values for X and Y “= B1+4*B2+B3” where B1 is the value in the first line, B2 the value in the second line and B3 the value in the third line of data in the Y column.
Copy the data into the odd numbered cells in your table. Select the cell you have just calculated by right clicking the mouse over the highlighted area, selecting copy and then right click and paste into the next odd numbered cell, continue until all the odd cells in your data table have the calculation entered.
Enter the formula “=SUM (D1:D10)” under the calculations you have just copied in the D column where D1 is the first figure and D10 the last figure you have just calculated (if you have more than 10 rows of data you would enter D then the row number of the last row in your table). This will give you the area under the curve using Simpson’s 1/3 rule.
Simpsons 1/3 Rule
Tips and warnings
- Simpson’s 1/3 rule only works if the X axis increases are equal and you have an odd number of data points.
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