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The general idea of the method is to set an integral equal to the function of an arbitrary variable in order to differentiate with respect to that variable and receive an integral that is easier to integrate. However, instead of using Feynman’s to set F(t) equal to the integral in the problem and differentiating it to get an easier integral, we can set F(t) equal to an easier integral and differentiate it to get the integral in the problem. | The general idea of the method is to set an integral equal to the function of an arbitrary variable in order to differentiate with respect to that variable and receive an integral that is easier to integrate. However, instead of using Feynman’s to set F(t) equal to the integral in the problem and differentiating it to get an easier integral, we can set F(t) equal to an easier integral and differentiate it to get the integral in the problem. | ||
| − | For example, let's take the integral: | + | For example, let's take the integral in the video: |
| + | <center><math> \int_{0}^{1}(\ln{x}) dx</math></center> | ||
[[ Walther MA271 Fall2020 topic14 | Back to Feynman Integrals]] | [[ Walther MA271 Fall2020 topic14 | Back to Feynman Integrals]] | ||
Revision as of 20:26, 30 November 2020
Application of Feynman's Technique
Even though the main concept of this technique has been covered in the What is Feynman's Technique page, there are many extensions of this technique and its uses. One of these applications is brought up by "Mu Prime Math" in his video about Feynman's technique.
The general idea of the method is to set an integral equal to the function of an arbitrary variable in order to differentiate with respect to that variable and receive an integral that is easier to integrate. However, instead of using Feynman’s to set F(t) equal to the integral in the problem and differentiating it to get an easier integral, we can set F(t) equal to an easier integral and differentiate it to get the integral in the problem.
For example, let's take the integral in the video:
