Quandaries and Queries

Level: Secondary

Question:
hi
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

Hi,

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.

Penny

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