It is shown that solving problems related to conics using Simpson’s 2nd compound rule is
an efficient numerical integration method. This work aimed to show the accuracy of this
method compared to the use of analytically solved problems, since some problems have
complex analytical solutions. During the studies, the fundamental concepts of the theory
were explored and Simpson’s 2nd compound rule was applied to approximate definite
integrals associated with conics, dividing the interval into smaller subintervals, to obtain
a precise result. When applying this method to problems of areas, volume of revolution,
surface areas of revolution and areas of length, it was noted that the results were satisfactory, as the errors obtained were within an acceptable value for the problems analyzed
and as they increased -the number of subintervals brought the function even closer to the
analytical solution, thus proving the reliability of the numerical method used.
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