Quandaries and Queries


Who is asking: Student
Level: Secondary

i used excel to find the area under a graph instead of integrating the function the analytical way. These are the different answers i got with different width of the x-values, the smaller the x-increment gets the more precise the area is when compared to the answer obtained the numerical way. I have trouble seeing why the answers i get is getting bigger and bigger and not smaller can someone plz explain?

Area under curve (in area units):

x-increment Approximate area
1 11.2187436
0.5 11.4302568
0.3 11.5484789
0.25 11.6127904
0.1 11.7361791
0.05 11.7793645
0.01 11.8146327
0.005 11.8190861
0.001 11.8226559
0.0005 11.8231026
0.0001 11.8234600
0.00005 11.8235046





I don't know what function you are integrating but it looks to me that what you have done is correct. If possible I would add another column to the table. If you can integrate the function and calculate the area analytically to find the actual area then add a column which is the absolute value of the difference between the actual area and the approximate area. The numbers in this column should get smaller.



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