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Invoking the Gamma Function 

Prime Newtons
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This definite integral could not be evaluated using the integration techniques learned in calculus2. I showed that the problem could be modified by appropriate substitution to facilitate the use of the gamma function for its evaluation.

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21 авг 2024

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Комментарии : 30   
@user-zv1no8xx2l
@user-zv1no8xx2l 2 месяца назад
Sir i solved this question at my first attempt and i used a substitution and then applied by parts and it was very easy to solve this . Thnks for sharing these interesting questions. My wishes to you from India
@sandyjr5225
@sandyjr5225 2 месяца назад
However, I believe (in any case) you should somehow know the area under the curve of e^(-x^2) dx from 0 to +inf.
@maxhagenauer24
@maxhagenauer24 2 месяца назад
I cant figure out what you did. If you let u = ln(1/x) then you get du = -1/x dx which is pointless. What did you do?
@mathematics_rudrarajprayag
@mathematics_rudrarajprayag 2 месяца назад
Amazing Video ❤❤❤ I am one of your subscriber from India .... Keep uploading such nice vids❤
@Ice_Screamer
@Ice_Screamer 2 месяца назад
You the goat fr
@RyanLewis-Johnson-wq6xs
@RyanLewis-Johnson-wq6xs 11 дней назад
Input integral_0^1 log(1/x) dx = 1 Result True
@Samir-zb3xk
@Samir-zb3xk 2 месяца назад
(0 to 1) ∫ [ln(1/x)]^(n-1) dx is an alternate form of the gamma function
@giorgiobarchiesi5003
@giorgiobarchiesi5003 2 месяца назад
Hi, very nice video, extremely elegant solution. But I have a question: when you move to the left part of the blackboard, you seem to stay very close to the blackboard itself; is there an obstacle we don’t see? As I watch more and more videos of yours, my curiosity is gradually tending to infinity! 😊
@PrimeNewtons
@PrimeNewtons 2 месяца назад
Good observation. There is an obstacle. Someday, I hope I will be free. Free at last!
@Zerotoinfinityroad
@Zerotoinfinityroad 2 месяца назад
Hello sir ..lots of love from India ❤❤❤ Can you please solve the trigonometry question I sent you please dear sir❤❤❤
@user-yd4ky5vb3w
@user-yd4ky5vb3w 2 месяца назад
Thanks for an other video master.
@user-xd8yu4wc5z
@user-xd8yu4wc5z 2 месяца назад
Keep going my guy
@victor1978100
@victor1978100 Месяц назад
I quickly solved this problem by knowing that the square root of ln(1/x) is the inverse function of e^(-x^2).
@Abhay0505
@Abhay0505 2 месяца назад
Epic ❤
@maxborn7400
@maxborn7400 2 месяца назад
this was an interesting one. Was not expecting sqrt(ln(1/x)) to transform into a Gamma integral
@maxvangulik1988
@maxvangulik1988 2 месяца назад
it may as well be the inverse of e^-x^2
@maxvangulik1988
@maxvangulik1988 2 месяца назад
y=sqrt(ln(1/x)) y^2=ln(1/x) e^y^2=1/x e^-y^2=x ye it's straight up just the inverse, which means you can use the following inverse function integration by parts formula: int(f^-1(x))dx=xf^-1(x)-F(f^-1(x))+C
@Fred_Ho882
@Fred_Ho882 2 месяца назад
I was wondering if you could teach some examples of mathematics that can be used in artificial intelligence
@PrimeNewtons
@PrimeNewtons 2 месяца назад
I will need to learn it first
@Fred_Ho882
@Fred_Ho882 2 месяца назад
@@PrimeNewtons Yes, never stop learning...
@Malcolm642
@Malcolm642 2 месяца назад
Hello Mr. I'm University student in Ethiopia and first I want to thank you for your supportive videos and i want to ask you a video request that's about limit and derivative from applied maths 1 we have an exam in next weak and we want a exam based video if you agree please let me know and I will send you our course outline THANKYOU and sorry for my english😅
@RyanLewis-Johnson-wq6xs
@RyanLewis-Johnson-wq6xs 11 дней назад
I did it in my head.
@surendrakverma555
@surendrakverma555 2 месяца назад
Thanks Sir 🙏
@technicallightingfriend4247
@technicallightingfriend4247 2 месяца назад
Answer is also interesting √π/2 is half guassian integral
@KPunktFurry
@KPunktFurry Месяц назад
0:17 understood nothing but it is going to be funny :D 1:20 and one question can you please use brackets for things like integrals, sums, and such symbols i am everytime so confused to dont find them 2:04 if you say that 5:26 and also please use brackets if you multiply negativ numbers!!!! 6:02 it should work now 7:07 ok i still just understand the healve but ok 8:44 great! LG K.Furry
@nizamkanchon3311
@nizamkanchon3311 2 месяца назад
Hello brother, u have been a great help. I have a favour to ask, if u could provide me the pdf of aops introduction to algebra solutions manual i would really be grateful.
@SAR1965
@SAR1965 Месяц назад
x+xy+y = 11 x2y + xy2 = 30 0:28
@brycenbg9372
@brycenbg9372 2 месяца назад
Wolfram alpha: Integral of sqrt[ ln(1/x) ]dx = x sqrt[ ln(1/x) ] - (1/2) sqrt(pi) erf { sqrt[ ln(1/x) ] } + C , Wolfram alpha is the real goat 💀
@comdo777
@comdo777 2 месяца назад
asnwer=1 oo pie
@comdo777
@comdo777 2 месяца назад
asnwer=pie 2 isit what
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