I saw Michael Penn do this the other day where he replaced a single definite integral with 3 nested definite integrals. I followed the steps, but I looked at it and wondered "How in the world would you know when you can apply this?" The 4 constants used as limits weren't nice and symmetrical like your example, and there wasn't any obvious symmetry, although he got it there, a definite integral at a time. Your example was a good one - it showed that if you have the difference of two functions that are identical except for a constant, or you can hammer it into the form f(x, g(cow)) - f(x, h(your mother)) through mathematical manipulations, you can try to apply this technique. Whether it results in a final definite integral that you can solve in closed form, or whether you can justify swapping the order, is still unknown until you actually see what you get.
This video was very enjoyable; gave me a lot of classic Flammable Maths vibes from my high school days, when I'd watch your integration videos everyday.
So.....we've both made multiple videos on this trick.....like applying a Laplace transform to an integral function to solve it.....and evaluating integrals using fubini's theorem by which we can switch up the order of integration.....and the fact that michael penn also made a video on this.....and I have an entire playlist on Feynman's trick.....and its still a well kept secret????
I did this integral with differentiation under the integral sign. Breaking the integral into two parts, one is a function of a and the other of b. The differentiate with respect to a and b respectively and then integrating back. Taking the sum of the teo solutions we have an integration constant left, but the total function is log((b+1)/(a+1))+C. Comparing this to the original integral and letting a=b for both we get C = 0 and thus the integral is log((b+1)/(a+1)). There might have been an unjustified step here but Im not too concerned about that rn, it worked.
6:49 I understand not remembering where you've heard something, or if you're making it up. It is difficult to track where knowledge is acquired after a lot of study. Our brains get tripped up naturally too.
I also know that saying, "differentiation is craft, integration is art". A lot of physics professors at the university i'm at say that, so Flammy most likely heard that from professors as well. I just don't know if it's an universal saying or if it's a German thing :D
Would also be possible to just add and subtract 1 right from the start, to create the Integral you solved a few days ago with respect to a and b respectivly :)
Can someone elucidate this concept to me, why do good mathematicians always use log instead of ln for the natural logarithm? It makes it more confusing
Worst 87 piece Star Wars X-wing Lego assembly guide I’ve ever seen. You barely showed the 87 piece Star Wars X-wing at all.
sry :'(
I saw Michael Penn do this the other day where he replaced a single definite integral with 3 nested definite integrals. I followed the steps, but I looked at it and wondered "How in the world would you know when you can apply this?" The 4 constants used as limits weren't nice and symmetrical like your example, and there wasn't any obvious symmetry, although he got it there, a definite integral at a time. Your example was a good one - it showed that if you have the difference of two functions that are identical except for a constant, or you can hammer it into the form f(x, g(cow)) - f(x, h(your mother)) through mathematical manipulations, you can try to apply this technique. Whether it results in a final definite integral that you can solve in closed form, or whether you can justify swapping the order, is still unknown until you actually see what you get.
I wanna see Michael Penn's video now
papa flammy is always there to fulfil our curiosities
Wow super cool! I love learning about all of these different integration tricks.
This video was very enjoyable; gave me a lot of classic Flammable Maths vibes from my high school days, when I'd watch your integration videos everyday.
So.....we've both made multiple videos on this trick.....like applying a Laplace transform to an integral function to solve it.....and evaluating integrals using fubini's theorem by which we can switch up the order of integration.....and the fact that michael penn also made a video on this.....and I have an entire playlist on Feynman's trick.....and its still a well kept secret????
Well he's not exactly gonna make a video about the hooker Feynman killed
That one random hard problem on the calc exam....
I love the xnopyt-esque code for the shop
I did this integral with differentiation under the integral sign. Breaking the integral into two parts, one is a function of a and the other of b. The differentiate with respect to a and b respectively and then integrating back. Taking the sum of the teo solutions we have an integration constant left, but the total function is log((b+1)/(a+1))+C. Comparing this to the original integral and letting a=b for both we get C = 0 and thus the integral is log((b+1)/(a+1)).
There might have been an unjustified step here but Im not too concerned about that rn, it worked.
If a
It's just a single point it doesn't change the integral.
😅
@@Noam_.Menashestill good to take note of
Covered this technique in Measure theory class. Haven't used it since lol (but that's because pure math don't calculate many integrals)
6:49 I understand not remembering where you've heard something, or if you're making it up. It is difficult to track where knowledge is acquired after a lot of study. Our brains get tripped up naturally too.
I also know that saying, "differentiation is craft, integration is art". A lot of physics professors at the university i'm at say that, so Flammy most likely heard that from professors as well. I just don't know if it's an universal saying or if it's a German thing :D
is there some book wherein one can find exercises to practice application of this?
That's such a sexy technique oh lordie.
Would also be possible to just add and subtract 1 right from the start, to create the Integral you solved a few days ago with respect to a and b respectivly :)
That's a nice little trick!
U differentiate under the integral sign, I integrate under the integral sign. We are not the same lol
papa (flammy's) got a brand new bag
you forgot the absolute value in the last integration otherwise good job
bro came into frame doing ballerina work 😂
8:20 it's a monomial
4:00 can’t you just differentiate with respect to t
Who else thinks this should drop on some merch asap? 🔥
neat!
Can someone elucidate this concept to me, why do good mathematicians always use log instead of ln for the natural logarithm? It makes it more confusing
True
I always love a tasty inte-garral 👌😷
7:40 Yeah just Fubini the shit
Keep it up ❤
very nice! Feynman rocks! as i heard he was a tricky bastard to find integrals;))
A feyn video indeed
at the beginning i thought the exponents were supposed to be 6 and 9
:^)
And people apparently believe you have vouchsafed this "well kept secret" until a time where you can optimize ad revenue with it's release.
I really really really want to get the watch, but I'm broke rn.
Thomas calculus question
What?
@@PapaFlammy69 Thomas calculus question, obviously.
@@PapaFlammy69 haven’t you heard about Thomas calculus question? It’s the hottest new trend in the maths community
I looked it up there’s a textbook called thomas calculus. Shitpost ass title ☠️
Thomas calculus question
Every day we stray further from god
Mum ?