Feynman's Integral Trick with Math With Bad Drawings

Richard Feynman famously used differentiation under the integral sign to solve many difficult problems, including one during his time at Los Alamos Laboratory during World War II that had stumped researchers for 3 months.

Learn how Feynman's Integral Technique works from Oxford Mathematician Dr Tom Crawford with the help of Ben Orlin from Math With Bad Drawings and his brilliant cartoons.

Produced by Dr Tom Crawford at the University of Oxford.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

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[malignusvonbottershnike]

It's the end of the day on Christmas day, and I'm watching a maths video. It is honestly so incredible that I've finally reached a point where I can understand all the interesting stuff I've been seeing for months on the maths side of YouTube, now that I've properly studied it. Thank you for videos like these, they're the reason I love maths so much.

[mehulchakraborty_]

I find you very expressive, like my maths teacher never used to move the hands, speak in an enthusiastic way, rather he had a machine voice and was dead serious . I discovered you today and I really admire your style of teaching

[TheBigBawsss]

Never expected machine gun kelly to explain Feynman integration technique, but here we are

[patrickhehl]

I think this is one of the first math result where my eyes legitimately widened when the final box was drawn around the n! equation (and I'm a final year engineering student so I've seen plenty of neat results!) Thanks for the crystal clear explanation Tom - I had seen this formula before but the derivation really made it click. All the best from McMaster University in Canada.

[gavcooper]

This is great. I feel like he talks about this very briefly in 'Surely You're Joking, Mr Feynman' but I've never seen an explanation of it that I could particularly get my head around until now. Thanks!

[woodrow-]

the way he makes calculus interesting and not boring to a high school kid that hasn't done anything past the required algebra classes is amazing. I literally understand nothing that is happening but it must be really cool if you understand it!

[tomgargan]

Wow, such a simple and amazing trick. Thanks for such a great explanation <3

[ashishrathorearx]

Respected Dr. Tom! You always remind me of my one friend who left me after the graduation. 🥺

[theimmux]

What a way to link teaching a new integration method with something interesting in math. I had heard of the Gamma function and its sibling before but had never quite understood how they were exactly connected to factorials.

[meiwinspoi]

refreshingly different. loved it. wondering why you did not utter the word “granmmmaaa” function.

[astroandriodrox]

I loved your the explanation to this example. I’m sure any electrical engineers or maths majors watching will immediately think of how similar this example is to the Laplace transform, which uses similar proofs for some of the standard transforms.

[rjmorpheus]

My mind is blown....this deserves a follow!

[johnchessant]

One of my favorite "differentiation under the integral sign" problems is sin(x)/x, from 0 to infinity. You do it by defining
I(a) = int sin(x) exp(-ax) / x.
Then differentiate w.r.t. a, which gives a closed-form for I'(a), which you then integrate to find I(a). Finally set a = 0.

[daphenomenalz]

My teacher of my tution during my school actually taught this and never told us it was feynmann's technique, he just said it's a better of doing integral that are similar to integrals you know already. He also said that it won't be asked in exams but still learning it would be helpful.

[karimalramlawi]

This is also called the laplace transform of x^n when s=1

[neruneri]

This is beyond my understanding and education level, but you're such a good presenter that I'm happily watching nonetheless. Have to say, I greatly admire you and your enthusiasm in communicating maths! While I struggle to follow along with maybe even most of your videos, some of them have nonetheless made it click for me and I've come away with more understanding than I had before, and that is deeply appreciated!

[imnotdeadinsideiswear]

this was satisfying im literally bursting with happiness

[JirivandenAssem]

best video i've watched in august !

[antonbordwine]

I couldn't handle it so I subscribed just to see you more often. 😌

[noonesperfect]

Great explanation .... interesting story, Feynman itself is sure special kinda genius 👍