Richard Feynman is considered to be one of the greatest minds in physics, and has won many accolades as a result of his research in areas such as quantum mechanics and particle physics. However, I am interested in knowing about how Feynman first originated what is known as Feynman's Trick in Integral Calculus. What specifically inspired him to formulate this technique? What steps did he take to create his trick? I am particularly interested in any proof or verification he wrote for justifying this new invention. If there are any papers, articles or journals that document the steps of this endeavor, please leave links in an answer below. Thank you in advance!
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7$\begingroup$ Feynman did not originate it. $\endgroup$– Rodrigo de AzevedoCommented Jul 20, 2020 at 5:59
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$\begingroup$ Related: hsm.stackexchange.com/q/8132 and hsm.stackexchange.com/q/6219 $\endgroup$– Rodrigo de AzevedoCommented Jul 20, 2020 at 7:36
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$\begingroup$ Wonder how YACAS or MACSYMA do it? :-) $\endgroup$– Carl WitthoftCommented Jul 21, 2020 at 11:55
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According to the history given here, he didn't.
I had learned to do integrals by various methods shown in a book that my high school physics teacher Mr. Bader had given me. [It] showed how to differentiate parameters under the integral sign — it’s a certain operation. It turns out that’s not taught very much in the universities; they don’t emphasize it. But I caught on how to use that method, and I used that one damn tool again and again. [If] guys at MIT or Princeton had trouble doing a certain integral, [then] I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.
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1$\begingroup$ The author of that Medium post condensed this excerpt from Feynman's book in exactly the same way I did at the start of kconrad.math.uconn.edu/blurbs/analysis/diffunderint.pdf: a couple of paragraphs were cut out in the same way using "[It]" and a few sentences were cut out in the same way using "[If]" and "[then]". It's almost as if the writer of that post did not actually look at Feynman's book directly and thought the inserted words [It], [If], and [then] that I used were part of what Feynman wrote. $\endgroup$– KCdCommented Jul 25, 2020 at 16:19
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$\begingroup$ "... almost as if ...", forsooth! :) $\endgroup$ Commented Aug 15, 2022 at 18:08