Good luck!

Wholesome

Why

@@Dark_kittens123 why not

@@thepuzzlemaker2159 why not not?

I didn't quite understand this method could you explain more

@@zaidabbassi6598 same. 😭

Genius

@@Sacchidanand g(x) is inverse of f(x) . integral of g(x) from a to b = a*b - integral of f(x) from a to b.

@@chromaxetian496 i tried this with e^x and ln x and it didn't work?

Can we integrate wrt to a const?

@@deekshanaik2438 no.

@@deekshanaik2438 No,we can't integrate with respect to a constant because definite integration involves summing up infinitely many rectangles, each representing an infinitesimal change in the variable we're integrating with respect to. However, if we were to integrate with respect to a constant, there would be no possibility of infinitesimal change because the constant remains constant by definition. Therefore, we wouldn't be able to conform to the intrinsic properties of definite integration, making integration with respect to a constant impossible.

Well said!

@@BriTheMathGuy I really enjoyed that video. Thanx

Glad it was helpful!

The second one is a fun trick, but it is usually worse than substitution. It only simplifies things if you are lucky. In his example, replace the 4 with any other number and it doesn't actually make the problem any simpler. The fastest method (as long as you have the first few rows of Pascal's Triangle memorized) for that problem isn't any he mentioned, it's using the binomial theorem to expand.

Which grade you are reading

@@generaldier1909 Me? At the end of physics Bachelor

At Which grade you have learn integration at first.

@@generaldier1909 usually in the first semester you take calculus 1 where they teach you integral (much more advanced than school ) in the second sem you take calculus 2 where you heavily use integral and double integral , and in calculus 3 you use it but kinda less then calculus 1 and 2 , but you continue using integral in your whole degree and almost in every subject and you hate your life and you start searching for other major where there is no integral then its turn out that almost every technology , science , engineering major teach calculus 1 and 2 so you start hating you life more because you dont want to go the law school wish is almost the only degree with no calculus so eventually you force yourself to memorize every single integral and limits that ever existed and you finally pass the calculus exam after 10 years of studying maths but you realise that you waste your life and you wont even use it in your life ... so yeah i feel sorry for you and for the humanity because such a subject destroying people lives

Yes, and proof

The first is prooving by doing u-substitution with inverse f and do integration by parte. The second is prooving by doing u-sub with (a+b-x). The third is by doing a line integral over a vector function , where "k" is your parameter. Then you express this integral as a double integral from x = [a,b] and y = [k, inverse of F(0)]. If you take the partial of y in the double integral, you end up with F(b,k) - F(a,k), which is correct. "F" is the function integrated only with respect to x.

Ya

Didn't feynman also just stumble upon it while self learning calculus from an old book?🤔

@@anikmandal9900 Yes, book by Woods (I've forgotten his name) given to Feynman by his teacher

Papa flammy's gonna be mad

@@anikmandal9900 I think it was originally invented by leibniz

What other tricks did you learn?

average jee aspirant 🗿

Thanks very much! I took your advice and added it to the playlist :)

Glad you thought so. Have a great day!

They ate not writing backwards. Think logically. They made a video where they are writing normally and that makes the text backwards to us. But they edit the video such that it becomes laterally inverted. That is why he is writing with his left hand.

@@TheLighthouse121 rwhoosh

@@ItamiPlaysGuitar r whoosh

@@ItamiPlaysGuitar You need therapy

You're welcome 😊

Hahahaha

Beautiful laura

😂

😂

Make the 66 teachers

Appreciated!

Glad it was helpful!

Glad you enjoyed it! Have a great day!

I suspect that they are not exactly the same and that you need both. If I understand correctly, the "Leibniz rule" is what Brian stated as "the trick", but in reality the "trick" is to parametrise the given integral using y so that applying Leibniz rule will give something doable, and this part is "Feynman's integral trick".

@@MichaelRothwell1 Feynman said himself that he took the so called "Feynman's trick" from a book (Wolf??) explicitly from the "Leibniz rule for differentiating under the sign of derivative"...

@@breakingmath1 Fair enough, thanks!

I think a better interpretation is transform a line integral in a double integral

Probably not, why don't you try it on a few complex functions using wolframalpha?

Leibniz is the original inventor, Feynman popularised it!!!

Glad you liked it!

Thank you! Cheers!

Thanks!

Most welcome!

Welcome!

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Nice!

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Thank you! 😃

If u dedicate 3-4 minutes per lesson period it might just work for a trick per lesson. This man did 3 in 11 mins 25 secs😅 just being an advocate for those brighter ones😁

@@truescalefpv4089 It depends on the audience to what extend I can step outside the boundaries of curriculum

​@@truescalefpv4089 The time allotted is very different when you are teaching something for the first time. Here everyone knows how to differentiate by parts. When this would be taught in class, it would take students far more time to get up to speed, and during the unit on techniques of integration, they are already tapped out on all the different techniques and their nuances. I can guarantee you, it would not be 3 or 4 minutes.

Very cool! Thanks for watching and have a great day!

@@BriTheMathGuy yes... it's really nice...love your videos...

Kazi Abu Rousan thank you very much!

This is also the Leibniz rule for integration

Can you please tell me how to solve integrals using Laplace transformation . I don't know that much about it but I know one thing that it is used to calculate differential equations . But how to solve integrals ?

Thanks!

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The first trick works with any inverse so long as you will be able to end up integrating it. The second trick will work for any function so long as it's defined for the appropriate values. For the third trick, I don't know if there is one way that will always work, sometimes it might be obvious and sometimes you might just have to try some different ways. I hope that helps!

The third trick is a thinking trick that was developed by Leibniz and popularized by Richard Feynman. Essentially what you want to do is, if you are clever enough, find the solution to a more general problem that involves your specific integral. Then you can find the answer. But you cannot use it for indefinite integration. Another example is the Dirilecht integral: Ssinx/xdx

Luis M same thing

Thanks!

Glad it helped!

By your name, I'm guessing you're Indian, we use that method as a standard method in NCERT

@@marvel.studios Oh that's soo cool I am in class 11 ryt now

@@marvel.studios I know that hahaha, it is cool 🤣😅

@@b.h.shashaank8713 your in 11th then why are you watching this video 😂

It is easier if you know what the derivative of arccosine is! 🤣

book from Richard D Prima

Not only in india but around the world its known as the king rule

That's great!

Great to hear! Thanks for watching and have a nice day!

BriTheMathGuy Thanks! Keep doing great job.

For anyone who might be interested in this integral: There is no anti-derivative for this integral, so I took a different approach and went after it numerically. I used Simpson's Rule (more accurate than the trapezoidal rule), with an n value of 12. Tedious, to be sure but, with 12 partitions, I got an approximation of -1.6. Graphing shows the preponderance of the area involved is indeed below the x-axis, so I trust the negative result. I then used 2-point Gaussian Quadrature, also got -1.6 (with just 2 points instead of the 12 used with Simpson's!) a true error value of accuracy 96.2%. Interestingly, if the f(a + b - x) substitution is used, the result is 0, which of course, is wrong. However, if the integral is "reversed," that is, instead of (x cos x) / (1 + sin^2(x)) one writes (x sin x)/(1 +cos^2(x)), then the f(a + b -x) substitution works, (following a bit of u-sub) giving pi^2/4.

1 + cos ^2x i think stems from cos ^2 + sin ^2 = 1. that way you change your derivative. so have you tried this substitution x(1 - sin (x))/1 + sin^2x oh btw there's a video on a channel called 'let there be math' about deriving sinusoidal functions with odd powers multiplied by unknowns, see if that helps

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glad you liked it!

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well you want to identify the part of the original integral that is troublesome-the part that sucks basically in that integral we hate having lnx in the denominator so we want to substitute(or multiply in certain cases) with something that would cancel lnx another classic example is the integral of sinx/x if you set a function f(t)=sintx/x and do the trick differentiating with respect to t you get the integral of xcostx/x and the x's cancel out and then you proceed as shown in the video that's why i said you multiply sometimes

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Thanks! Have a great day!

Great point!

None of what you say is true. Since both x^5 -1 and lnx are negative at (0,1), their quotient is positive. Furthermore, it reaches a well defined limit at the endpoints and it's continuous throughout the interval, hence the improper integral is convergent.

Same, I’m in isc

Kings property

No.

Welcome!

Maybe he's writing backwards on a clear pane of plastic between him and the camera?