You'll be pleasantly surprised by this one. If you like the channel, consider supporting me on Buy Me A Coffee using the following link: www.buymeacoff...
A classic use of symmetry, good one! Integrals like these are great because they look absolutely impossible at first, but once you learn the trick they're a piece of cake. Integrals of this form were one of my first introductions to integration techniques beyond those taught in standard calculus classes for that reason.
Careful: treating an improper integral as symmetric is only valid if you already know it converges. In this case, the exponential in the numerator ensures that, but it's worth justifying.
Thumbs down for the ads. For the bee: i didnt see it. I wanted to see a bee or better a whole swarm of bees. I find the title deceptive, promising bees where no bees are.
Nice. When I saw the expression my first thought was "this is so complicated", and my second thought was, "surely this is too complicated to be solved any other way, it MUST be some kind of even-odd function symmetry trick, that's the only way this would be on a contest".
Wow that is a freaking wild integral. Curious do you have a favorite math book? Especially in analysis? I think my favorite hard math book is Michael Artin's Algebra, and my favorite laid back book is The Gamma Function by his dad Emil Artin haha. My analysis classes were with Baby Rudin and then Royden though and didn't particularly like either book.
0:45 Before writing I=... you need to prove that this improprer integral converges. Also at 6:34, you cannot write explicitely ∞ at the bound, it isn't a number. You need to uses the limit. I hope this can improve your next videos. Apart of these little remarks, great technic for obtain the final result.
This isn't a Real Analysis class, so those points are of little importance to this video. A proof of the convergence of this integral is trivial and careful limiting is implied in his notation, he's just using a shorthand.
I see your point but it wouldn't improve the video I think. The convergence in the first case is obvious at the level at which this video is directed to. The second one, the infinite limit of integration, comes from the former; since it converges, it coincides with it's principal value (limit of the integral from -a to a with a going to +infinity), that's the other integral from 0 to a and that converges to the integral from 0 to +infinity, withous issues since you are integrating something positive. All of this would only make for a longer video with no really ideas, just technicism which isn't required here.
*Challenge Integral* (a^2-x^2)^((1/2) +c)) from bounds 0 to a where c is 0,1,2,3... Note(s): *Do not evaluate the integral by taking specific values of c.* *There must be a better and more specific solution for this integral.* *I do not understand Beta, Gamma functions, but I still managed to solve it to get at least a general solution.* HINT: *My answer contains Infinite Product.*
A classic use of symmetry, good one! Integrals like these are great because they look absolutely impossible at first, but once you learn the trick they're a piece of cake. Integrals of this form were one of my first introductions to integration techniques beyond those taught in standard calculus classes for that reason.
A great use of the King's Property of Integration. 👍
que horror de caligrafía
It's a very amazing and very cool improper integral .
It's almost magical that the integral doesn't depend at all on the denominator.
And the proof is surprisingly satisfying
Careful: treating an improper integral as symmetric is only valid if you already know it converges.
In this case, the exponential in the numerator ensures that, but it's worth justifying.
Wonderful integral
Thumbs down for the ads.
For the bee: i didnt see it. I wanted to see a bee or better a whole swarm of bees.
I find the title deceptive, promising bees where no bees are.
Nice. When I saw the expression my first thought was "this is so complicated", and my second thought was, "surely this is too complicated to be solved any other way, it MUST be some kind of even-odd function symmetry trick, that's the only way this would be on a contest".
Wow that is a freaking wild integral. Curious do you have a favorite math book? Especially in analysis? I think my favorite hard math book is Michael Artin's Algebra, and my favorite laid back book is The Gamma Function by his dad Emil Artin haha. My analysis classes were with Baby Rudin and then Royden though and didn't particularly like either book.
0:45 Before writing I=... you need to prove that this improprer integral converges. Also at 6:34, you cannot write explicitely ∞ at the bound, it isn't a number. You need to uses the limit. I hope this can improve your next videos. Apart of these little remarks, great technic for obtain the final result.
This isn't a Real Analysis class, so those points are of little importance to this video. A proof of the convergence of this integral is trivial and careful limiting is implied in his notation, he's just using a shorthand.
I see your point but it wouldn't improve the video I think. The convergence in the first case is obvious at the level at which this video is directed to. The second one, the infinite limit of integration, comes from the former; since it converges, it coincides with it's principal value (limit of the integral from -a to a with a going to +infinity), that's the other integral from 0 to a and that converges to the integral from 0 to +infinity, withous issues since you are integrating something positive. All of this would only make for a longer video with no really ideas, just technicism which isn't required here.
wow thats really cool
odd and even functions are really useful huh
It was quite easy although it looked tricky at first glance, solved it in a minute
This is one of the easiest integrals you put in your channel, the recent ones are just 💀🔥
Though glad I sometimes solve few
I knew the trick. These integrals are kind of "artificial"
1/ln2020...il mio metodo è simile al tuo...io non ho usato le generalizzazioni come hai fatto tu... però il risultato è identico
Ne serite s tem
Love that instead of just solving, u inttoduced the pattern
Thank you for your work
What is the software you use for your vidéos ? Thanks
Nice. Papa Flammy did something like this a few years ago too
Yeah but his proof sucked so obviously I had to do something better 😂
as a jee aspirant i did this in a minute!!
thanks bruv
*Challenge Integral*
(a^2-x^2)^((1/2) +c)) from bounds 0 to a where c is 0,1,2,3...
Note(s): *Do not evaluate the integral by taking specific values of c.*
*There must be a better and more specific solution for this integral.*
*I do not understand Beta, Gamma functions, but I still managed to solve it to get at least a general solution.*
HINT: *My answer contains Infinite Product.*
That's fricking amazing.
Excellent !!
❤
Fantastic !
Bruh That was freaking insane, I always end up learning something new from your vids lol
I see you corrected it after my comment, good job!
This is JEE level easily 😂
???? It was on the easier side
I don't know what you people get after showing off every time
Wow! nice technique!
0:05 Form zero
That was beautiful explained, thank you!
That was awesome! Thanks for taking the time to prove the general result, really gives insight into the problem!
Yeah the only fun thing about today's video was the proof and its actually 🔥🔥🔥
Write numbers and words properly
Do you expect your somewhat rude comment to trigger any response or change? For real...
@@AT-zr9tv my nickname
@@AT-zr9tv why is this rude
It was really cool, but I dislike a such type of trick, it is too special for real physical problems