I appreciate you taking these integrals which sometimes seem random and then equating them to more famous mathematical creatures. It's also really great to follow along, work on the integral for a bit, then go back to the video to find you have taken the same step. Congratulations for 5000 subscribers. You've earned them : )
So, how does taking the derivative of an integral in respect to a different variable work? Like, is there a nice way to work it out, in general? Since in this you used the digamma to evaluate it.
Differentiation under the integral sign is a tricky one. If the bounds are constants then you can just take the partial derivative of the integrand, but if not it's much harder. Take a look at Leibniz's rule for differentiation under the integral sign for more on that. Typically differentiating the integral and then evaluating it is what you do when using Feynman's trick so there's some great examples of it in videos that use that. Hope this helps and thanks for the comment!
I appreciate you taking these integrals which sometimes seem random and then equating them to more famous mathematical creatures. It's also really great to follow along, work on the integral for a bit, then go back to the video to find you have taken the same step. Congratulations for 5000 subscribers. You've earned them : )
Thanks so much! I'm really glad you enjoyed.
for a second there, i thought this was a product integral because dx is in the exponent in the thumbnail
Great integral to wrap up the series! Congrats on 5k!!
Thanks! Glad you enjoyed it.
Love your videos, they are very helpful to me 🥰
Thanks! I'm really glad you like them.
I wish you had a bigger board.
Me too 😔
this is exactly how i did it, down to the variable names 😆 nice problem!
Nice!! Great minds think alike 😁.
Very clean
@@jcfgykjtdk Thanks!
Evaluate Sum{r=2 to ∞} (r(choose)2/(r+1)!)
I found it really cool
Wow! That was a great question. Is it 1/2(e-2)?
@OscgrMaths Yesss
Is there easier way than using eˣ taylor expansion and integrating x²eˣ to get the 1/(n+3) factor?
@alphazero339 Idk, maybe there is, I know 2 ways of solving it, both involving the Taylor series
Great job.
Btw, besides Feynman Techbique, How would you tackle Achmed’s Integral?
Integrate
So, how does taking the derivative of an integral in respect to a different variable work? Like, is there a nice way to work it out, in general? Since in this you used the digamma to evaluate it.
For taking derivative with respect to x of integral which contains x (either as bound or inside the integrand) google "Leibniz integral rule"
Differentiation under the integral sign is a tricky one. If the bounds are constants then you can just take the partial derivative of the integrand, but if not it's much harder. Take a look at Leibniz's rule for differentiation under the integral sign for more on that. Typically differentiating the integral and then evaluating it is what you do when using Feynman's trick so there's some great examples of it in videos that use that. Hope this helps and thanks for the comment!
Bro got 5000 subs but not 5000 square millimeters on his board
@zlodevil426 😓
t=tan(x)
I=int[-♾️,♾️](te^t•e^-e^t)dt
s=e^t
ds=e^t•dt
I=int[0,♾️](ln(s)e^-s)ds
I=Ř'(1)=-ř