The Error Function & The Integral of e^(-x^2)



In this video, I show you the graph of the Error Function, namely y=erf(x). This is a non-elementary function (or you can call it an advance function).

Check out how to sketch e^(-x^2), bell shaped curve,
And you can read more about
probability density function here:

error function here:

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blackpenredpen | 曹老師

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  • 08:30 By the fundamental theorem of calculus part I, it's the essential part of it .

    Stanley Jibson July 26, 2020 7:04 am Reply
  • dang mate really good explanation🙏

    Ni ls July 26, 2020 7:04 am Reply
  • We can also do it by series expansion.

    Technical Saurabh gyan July 26, 2020 7:04 am Reply
  • Please don't they use the Gamma function

    Solomon Bennin July 26, 2020 7:04 am Reply
  • Triple integral of the error function

    Pedro Dumper July 26, 2020 7:04 am Reply
  • Very good outline of handling the normal distribution function! And it would be interesting to provide and outline how to use theory of complex analysis to evaluate this integral!

    Saeid Alghamdi July 26, 2020 7:04 am Reply
  • Why would you make someone sit through a 3 minute ad?

    shebangsthedrums01 July 26, 2020 7:04 am Reply
  • I AM ERROR(*√π/2), PRESS ANY KEY TO RESTART

    Aneesh Srinivas July 26, 2020 7:04 am Reply
  • Awesomeness at peek..!

    Sarah Thomas July 26, 2020 7:04 am Reply
  • hello friend. How can I Integrate e^(ax – (x^2)/b) where a and b ara real constants? I have search a lot and I can´t get a solution

    Josue Jimenez July 26, 2020 7:04 am Reply
  • Hey!!
    Guys i've created a math channel
    Come check it out?

    6or9 July 26, 2020 7:04 am Reply
  • the error function is how we get sqrt(pi)/2 from the factorial of 1/2

    Raymond S. July 26, 2020 7:04 am Reply
  • It's a amazing integration and containing complex solution

    Akash Patel July 26, 2020 7:04 am Reply
  • Rai hier

    Felipe July 26, 2020 7:04 am Reply
  • This video helped me to understand better the second Fick's diffusion law. Thank you soo much.

    Rayane Campos Lopes July 26, 2020 7:04 am Reply
  • Isn't concave down called concave and concave up called convex?

    Loriana Mesia July 26, 2020 7:04 am Reply
  • Bro please make the volume of your videos uniform. Very helpful though. Thanks!

    John Daniel Villanueva July 26, 2020 7:04 am Reply
  • 3:53 WHERE DID blackpenredpen GO?? WHAT DID YOU DO WITH HIM??
    3:56 oh there he is

    GigaGiant Studios July 26, 2020 7:04 am Reply
  • Is this a pre req to flat erf theory?

    spim randsley July 26, 2020 7:04 am Reply
  • That's cheating though. The whole point is that area. If you just assume it's sqrt(pi), then there is really not much left to do.

    JanPBtest July 26, 2020 7:04 am Reply
  • I Subscribed to your channel , I'm 11 years old , and I like so much your videos with integrals !

    Ylli Morina July 26, 2020 7:04 am Reply
  • I knew something was wrong with this question when it took me 20 minutes to even try to start the problem after I gave up lol and here I see it's nonelementary -.-

    Syntax AVA July 26, 2020 7:04 am Reply
  • Does non elementary also mean you wont find a solution by substituting with U?

    Schelias July 26, 2020 7:04 am Reply
  • intlimits_t^x {frac{{{z^{theta  – 1}}}}{{1 – A{z^{theta  – 1}}}}dz}

    Bakhodirjon Toshtemirov July 26, 2020 7:04 am Reply
  • I've got this problem on a 12th grade test

    Nairobi July 26, 2020 7:04 am Reply
  • Thank you sir

    Spandan Padhee July 26, 2020 7:04 am Reply
  • If you don't know how use the erfi… is it right to transform the e^x^2 into a Taylor Series polynomial?

    e^x^2=∑ₖ₌₀ᢁ (x^2)^k/(k!) So ∫e^x^2 dx = ∫[∑ₖ₌₀ᢁ (x^2)^k/(k!)]dx

    If it's not wrong, how would o(x^n) be integrated? o(x^(n+1))/(n+1)??? Also, how'd it be differenciated?

    Thx for your amazing vids BPRP💚

    MisutāPurinsu July 26, 2020 7:04 am Reply
  • Well not all integrals go to infinity, what about defind domain? This video useless for that

    Den July 26, 2020 7:04 am Reply
  • ¿A esta integral se le puede llamar la Integral Gaussiana? ¿Si no es así, como se resuelve la integral de la película "Gifted"?

    Pizarrón JCPérez July 26, 2020 7:04 am Reply
  • your passion is contagious

    will howard July 26, 2020 7:04 am Reply
  • <3 love u

    will howard July 26, 2020 7:04 am Reply
  • Chen lu, yus my favorite lu

    Naved July 26, 2020 7:04 am Reply
  • All I see is the word sex

    Nicholas Villani July 26, 2020 7:04 am Reply

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