This famous integral is perfect for Feynman's integration technique

The legendary Dirichlet integral evaluated using Feynman's trick

[@maalikserebryakov]

By this point that thumbnail of feynman is appearing in my dreams

[@driesvanheeswijk1633]

Dude I love you. I've been loving the videos, you're putting in so much work and I really appreciate it

[@maalikserebryakov]

Deja vu

[@andikusnadi1979]

8:23 why (t+I) become 1 ? Thank you sir for the answer

[@andrewneedham3281]

We want the negative imaginary part of (t + i) divided by (t^2 + 1), right? Well, separating it into real and imaginary, we get t/(t^2 + 1) + i*[1/(t^2 + 1)]. The imaginary part is 1/(t^2 + 1) because we're stripping the i when we take the imaginary component. But then, we want the negative imaginary part, so that's -1/(t^2 + 1). I'm not sure why OP never bothered to answer your question, as it's a good one. I'm sure a lot of people were confused by that.

[@littlechar]

Would you say this video is a good way of understanding Feynman's Technique? I can't really find a guide anywhere

[@maths_505]

Indeed it is.... Along with my whole playlist on the topic ofcourse 😂

[@maalikserebryakov]

Same here I can't seem to figure out how to know where to place the parameter, or when to introduce an entirely new function of t. I've asked on forums and got the typical response of "do more practise problems bro. "

[@zathrasyes1287]

That's why people say: "Differentiating is a mere laborious technique, but integration is an art."

[@madhusyamala-n1t]

Wouldn't e**-tx collapse only if t is not zero as x goes to inf? But later we are substituting t as 0. How does that work?

[@maths_505]

We're letting t go to infinity That collapses the integral

[@andikusnadi1979]

at 3:35 you use 2 in front of integral , where is the 2 , i think the result must be multiply by 2.

[@andrewneedham3281]

The function sin x / x is an even function. For the definite integral of an even function, there's a very handy result: if your interval is symmetric you can just take half the interval and double the result to get your answer. This result can help in some nastier integration situations. OP showed the function was even when he plugged in (-x) for x and got the original function. He then used the result, but he wasn't explicit in telling us that he used the result, as it's fairly elementary given the other manipulations he was doing. Good for you for asking for clarification.

[@joshuawalsh6968]

7:30 e^0 times e^0 is 1 times 1 is 1 , then why did you put down a negative?? I keep scratching my head trying to work it out

[@maths_505]

Upper limit - lower limit ring a bell?

[@joshuawalsh6968]

Sometimes I stumble on the simpler parts of integral equations. I still can't see how it became negative from a limit of zero, I will sit on it for a few days till hopefully it jumps out at me. Absolutely Love your videos btw keep up the good work

[@maths_505]

Thanks mate

[@joshuawalsh6968]

how silly of me , lim - lim , lol

[@tbg-brawlstars]

7:10 can't we use by parts?, I got it by parts

[@maths_505]

Oh yes ofcourse but I just like invoking complex numbers whenever I get the chance.

[@tbg-brawlstars]

@@maths_505 Lol, keep up the good work, btw Feynman's Technique is not even in my syllabus but you've taught me that, I watched 4 of your videos on Feynman Technique Thanks!

[@yusuke4964]

I wonder how he conceived this idea…

[@maths_505]

Its from the book advanced calculus by woods. His physics teacher gave it to him in high school.

[@allenho2778]

I rather do a contour integration.

[@maths_505]

I did that in a compilation video a couple videos back...solved it using 5 different methods there😂

[@SleazyNice]

This is Leibniz's technique NOT Feynman's. Feynman took this from a book on Advanced Calculus. The real name of the technique is "Leibniz Integral Rule". To attribute this to Feynman is complete BS. He didn't come up with it. The book he got this method from as well a several other gems is: Advanced Calculus by Woods, 1926.

[@andrewneedham3281]

I mean, you're not wrong, but the technique was pretty niche until Feynman gave it a renaissance back in the day. So a lot of people call it "Feynman's trick" as shorthand. I don't think anyone was trying to take anything away from Leibniz, who is a great contributor to mathematics. Frankly, there are a ton of theorems in mathematics that have one person's name on them despite being proven by someone else, so if this bothers you, you probably shouldn't delve too deeply into math history.

[@SleazyNice]

@@andrewneedham3281 Too late, I've been ranting on these kinds of things for decades. Don't even get me started on Einstein, who I call "The Original Leonard Hofstadter". Everything thing he did was a derivative of someone else's work. Every time I hear the names of James Watson and Francis Crick when it comes the the Double Helix I go into a rage. LOL, such is life. I'm just passionate about the truth.

[@anubhabnaiya5051]

This techniq and this integral is becoming your signature sir💝🙇

[@maths_505]

Its basically the perfect integral for teaching Feynman's trick

[@maalikserebryakov]

Phull Sapport SAar

[@t.sambath]

Good teacher 🎉❤

[@MathOrient]

I'm curious about the various alternative methods available to solve this integral. Do you have any idea? :)

[@MatthisDayer]

maybe someone should do a video showing a couple of methods

[@maths_505]

Already did that a couple videos ago😂 5 methods there

[@MathOrient]

@@maths_505 ❤

[@MrJohnBos]

I lost you during the first trig substitution but I believe you. I was never good at calculus in college. I became a big fan of Richard Feynman after reading, "Surely you're Joking Mr. Feynman". I would love to have meet him over a beer , he was a fascinating character.

[@manstuckinabox3679]

bought a small notebook, going to write down each op technique here.

[@simran1-08]

Can you integrate 1/(1+x⁷) dx

[@MrWael1970]

Very nice video. Thanks.

[@andikusnadi1979]

Very well explanation