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=A Review on Reparametrizing=
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Over the past years in math, I've seen many different methods for reparametrizing variables as a way to make a complex integral easier to deal with. Essentially we just take a function of some value and differentiate it with respect to a different variable, creating newer, simpler functions. One application of this includes u-substitution, where we let an arbitrary variable (in this case "u") represent a portion of our integral. For example, let's take this integral:
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<center><math> \int {sinx*cosx} </math></center>
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, and we even see parametrization appear in surface integrals.
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Feynman's Technique to integration utilizes parametrization and a combination with other different mathematical properties in order to integrate an integral that is can't be integrated through normal processes like u-substitution or integration by parts. It primarily focuses on setting a function equal to an integral, and then differentiating the function to get an integral that is easier to work with. A simple example would be:
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(1/2)*xe^(x^2) instead of just e^(x^2).
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[[ Walther MA271 Fall2020 topic14 | Back to Feynman Integrals]]
