The hardest integral from 2022 BMT Integral Bee: th-cam.com/video/SxNXrL-_tYA/w-d-xo.htmlsi=miEQpyVcUqYwOlQB Get your Ultimate Calc 2 Integral sweatshirt here: amzn.to/3Cx7YMQ
Very nice solution. My calculus had bene getting a bit rusty after more than 30 years without using it, but seeing your videos over the past year has gotten my mind back in the groove.
LOL IM IN THE VIDEO. I've never used a chalkboard before (so you can't read what I even wrote) and I was too nervous for my eyes to even perceive the e^x, so I just integrated the fraction on instinct and got it wrong.
Another great problem to share with my students. As I tell my students, most integrals are rigged in your favor, and this is an excellent example of a problem written to work nicely,
I pretended the e^x wasn't there and did partial fractions, (then multiplied it back) resulting in the sum of 2 integrals. Then I did IBP on the second one allowing the integrals to cancel. Pretty cool integral.
This integration is pretty easy tbh. Just use u-sub and by-parts and voila. I used z = x + 1 and rewrote the Integral as this: int[ (z-2)*e^(z-1)dx/z^3] Simplified it by taking 1/e out and seperated the fractions as e^z/z^2 - e^z/z^3. Now Simply do by parts by differentiating z^-2 and Integrating e^z. After doing this once we observe that e^z/z^3 gets cancelled out and we are left with e^z/z^3 + c OR e^x/(x+1)^3 + C which is the answer!
This is a kind of standard question taught to students in 12th grade in india, so i could solve easily, but can understand if you see if for the first time under time pressure, you wouldnt get correct solution
Hi bprp, i wanted to ask you if you can make a video about the limit: lim (((-1)^j/j!^j)^(1/j)), because i don't know why on wolfram alpha the result is 1/sqrt(2*π),thank you!
Often the problems are specially constructed so that a trick like this will work. If you try to integrate a function that you found somewhere it could be very hard.
Wow, this method is wonderful and I did solve it but by substitution & by parts method. It was not lengthy at all. I solved it by substituting x + 1 = u, bringing everything in terms of u & then opening the bracket by multiplying the exponential term to each one of them. & then solving only the first integral in the R.H.S, I realised that a component of that result cancels the second integral in the R.HS. Then substituting back x+1= u, I got the desired result.😅
I didn't touch calculus for 2 years and I solved it within minutes during a psychology lecture🤣probably because I dare not to go for the complicated methods (partial frac) and accidentally found the pattern by looking at the DI table
when I first saw e^x I knew I had to use f(x)e^x but I forgot to do +and -1 ; but even then my real weakness is addition subtraction multiplication, heck I forgot long division 💀
So you're just gonna hope that the -2 term is gonna be the derivative of the 1st term? What if its not the derivative and you just wasted precious time ?
What is the point of calculus when it’s impossible to always get it right and costly to get it wrong? Too many rabbit holes. How is it possible to usually get the calculus right when it’s impossible to never get the algebra wrong?
The hardest integral from 2022 BMT Integral Bee: th-cam.com/video/SxNXrL-_tYA/w-d-xo.htmlsi=miEQpyVcUqYwOlQB
Get your Ultimate Calc 2 Integral sweatshirt here: amzn.to/3Cx7YMQ
Very nice solution. My calculus had bene getting a bit rusty after more than 30 years without using it, but seeing your videos over the past year has gotten my mind back in the groove.
LOL IM IN THE VIDEO. I've never used a chalkboard before (so you can't read what I even wrote) and I was too nervous for my eyes to even perceive the e^x, so I just integrated the fraction on instinct and got it wrong.
I just thought you had developped your own system to write math faster abd was almost in awe😅
Pro Tip: Less gaming, more math.
@@lambdaproggrow up 🐈
I think you f'ed it up being under pressure. Otherwise it's an easy one😅
You're the right one or the left one?
Another great problem to share with my students. As I tell my students, most integrals are rigged in your favor, and this is an excellent example of a problem written to work nicely,
Another great video from a great man
Beautiful solution! Simple is beautiful!
That was insanely easy atleast considering we were taught that property of (f + f') e^x
I pretended the e^x wasn't there and did partial fractions, (then multiplied it back) resulting in the sum of 2 integrals. Then I did IBP on the second one allowing the integrals to cancel. Pretty cool integral.
My mind literally
I looked for quotient rule and since that has a square at the bottom I multiplied by x+1 to get (x+1)^4. Then, I differentiated e^x/(x+1)^2.
This integration is pretty easy tbh. Just use u-sub and by-parts and voila.
I used z = x + 1 and rewrote the Integral as this:
int[ (z-2)*e^(z-1)dx/z^3]
Simplified it by taking 1/e out and seperated the fractions as e^z/z^2 - e^z/z^3.
Now Simply do by parts by differentiating z^-2 and Integrating e^z.
After doing this once we observe that e^z/z^3 gets cancelled out and we are left with
e^z/z^3 + c OR e^x/(x+1)^3 + C which is the answer!
Cool - congrats to the BMT winners!
This is one of our best teachers in the world!
wow I haven’t done calc in a while and this helped me touch up on my understanding, this integral worked out beautifully
Just learned a valid lesson. Great work. ❤
Thats a very hard to see reverse product rule!
Interesting integral and a great video.
Hey blackpenredpen, could you graph x^x for x
The reverse product rule is dope
Finally. U upload 😊😊. I also love math.
This is a kind of standard question taught to students in 12th grade in india, so i could solve easily, but can understand if you see if for the first time under time pressure, you wouldnt get correct solution
If you do the u-sub and do integration on parts on one of the integrals, the two integrals cancel out and leave the uv term
An interesting way to integrate functions with the exponential function ✨✨
this was easy quest like crying for e^(f(x)+f'(x)) type form
👍interesting, thank you
I maid a u-sub : t=x+1 then expressed e^x as a tailor series
It’s basically integrating product rule.
where can i get the questions? i practiced some from your instagram and they were really good
where does he teach? I think it would be great to take some of his calculus classes. It would be challenging.
I am in class 10th and I was able to solve this in less than 30sec
saw this as a shift 2 pyq
I had been trying since the video was published. I have just given up few minutes ago.
Woah I did this problem right 🎉
Hi bprp, i wanted to ask you if you can make a video about the limit: lim (((-1)^j/j!^j)^(1/j)), because i don't know why on wolfram alpha the result is 1/sqrt(2*π),thank you!
can you solve x^6=(x+1)^6
x=-0.5 is only solution in R
@@thatapollo7773You just did someone's homework.
@@robertpearce8394 Fortunately if it's homework, they have no work to show for credit
Good!
Admiro muito o seu trabalho blackpenredpen ❤
great sir
class 12 ncert maths
:(
This exact problem came to my finals in college😂
Managed to solve it as well. Tho i sacrificed time for another one.
Is Berkeley math integration bee have their webpage like mit integration bee??
You are from Berkeley, I mean you are a professor in Berkeley University right?
Really elegant solution, but how are you supposed to guess this? 😮
Thank you. And I would say experience definitely helps. I don’t think I can do it either if it was my first time seeing an integral like this.
Practice. Adding and subtracting numbers like that is quite common actually when solving integrals
Often the problems are specially constructed so that a trick like this will work. If you try to integrate a function that you found somewhere it could be very hard.
Hello
Please help me with this question x^3+16x-64=0
Method ÷ classic integral
I knew that it will use this identity, maybe I could've done it few months earlier from now 😅
Wow, this method is wonderful and I did solve it but by substitution & by parts method. It was not lengthy at all. I solved it by substituting x + 1 = u, bringing everything in terms of u & then opening the bracket by multiplying the exponential term to each one of them.
& then solving only the first integral in the R.H.S, I realised that a component of that result cancels the second integral in the R.HS.
Then substituting back x+1= u, I got the desired result.😅
❤❤❤
I didn't touch calculus for 2 years and I solved it within minutes during a psychology lecture🤣probably because I dare not to go for the complicated methods (partial frac) and accidentally found the pattern by looking at the DI table
when I first saw e^x I knew I had to use f(x)e^x but I forgot to do +and -1 ; but even then my real weakness is addition subtraction multiplication, heck I forgot long division 💀
This is my school question 😂😂 i got it😅😅
u= e^x/(x+1)²
du = (x-1)e^x/(x+1)³ dx
Integrate : 1 du = u + C
R = e^x/(x+1)² + C 😴
Did this in head....mit bee is much more fun tbh
Prove that lim((x-2)(x-3)/(x-4)(x-5))= 0 as x tends to 5.
Refer to graph and explain mathematical proof.😢
E
Orz
hello world
красиво
Which county are you from sir?
Class 12th NCERT
INTEGRALS CHAPTER 😊😊
kounn hay bee tuu
Your ex father @@malayameher5177
Your ex father @@malayameher5177
Yeah bro
@@malayameher5177 your Xfatherr
damn what the f
In India we 12th class students consider it as one of easiest questions
In India we learn this in class 12 lol
So you're just gonna hope that the -2 term is gonna be the derivative of the 1st term? What if its not the derivative and you just wasted precious time ?
first
Lol took 20 seconds.
Laugh out loud. You're a liar. Shut up.
@@robertveith6383 even a normal class 12 student can solve that in 20 seconds.
What is the point of calculus when it’s impossible to always get it right and costly to get it wrong? Too many rabbit holes. How is it possible to usually get the calculus right when it’s impossible to never get the algebra wrong?
?
Thank you for asking this. I thought I was just being an utter dunce!😂
branch prediction
Top ten most stupid comments
dude experiencing existential crisis...