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This is a joke that circulates from time to time.
So what’s the answer?
As usual, watch the video for a solution.
Or keep reading.
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“All will be well if you use your mind for your decisions, and mind only your decisions.” Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
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Answer To Viral PIN Code Problem
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
I would never have been able to solve this on my own. I found an interesting write-up by Claude Leibovici on Math StackExchange.
An integral that is a rational function of x and the square root of a general quadratic √(ax2 + bx + c) can be solved by an Euler substitution. There are a couple of forms, but the one useful in this problem is:
√(ax2 + bx + c) = x√a + t
In the denominator of the integral, the quadratic has a = 1, so we use the substitution:
√(x2 – 3x + 2) = x + t
Solving for x gives:
x = (2 – t2)/(2t + 3)
dx = -2(t + 1)(t + 2)/(2t + 3)2 dt
It is a huge calculation to substitute and simplify the integrand. But doing so gives:
2(t + 1)2(3t4 – 4t3 – 2t2 + 56t + 60)/(2t + 3)4
Note the limits of integration will change from x being 0 to 1 to t ranging from √2 to -1. Now make the substitution u = 2t + 3, which gives the new limits of integration as 2√3 to 1. Calculating the new du and t = (u – 3)/2, and substituting gives the integrand:
3u2/64 – 25u/32 + 317/64 – 135/(16u) + 317/(64u2) – 25/(32u3) + 3/(64u4)
Any calculus student should be able to find an antiderivative term by term as:
u3/64 – 25u2/64 + 317u/64 – (135/16) ln(u) – 317/(64u) + 25/(64u2) – 1/(64u3)
Evaluating from u = 2√3 to 1 gives:
(135/16) ln(2√2 + 3) – 101/(4√2) ≈ -2.98127
Presumably the PIN code is the first 4 digits, so it could be 2981.
References
Math StackExchange Claude Leibovici
https://math.stackexchange.com/questions/2814179/how-to-integrate-the-product-of-two-or-more-polynomials-raised-to-some-powers-n
Euler substitution
https://en.wikipedia.org/wiki/Euler_substitution
Reimann sum
https://en.wikipedia.org/wiki/Riemann_sum
Midpoint rule
https://commons.wikimedia.org/wiki/File:Riemann_sum_(middlebox).gif
09glasgow09, CC BY-SA 3.0
.gif){kind=link}
solution @NathMathTutoring
https://www.youtube.com/watch?v=F9ZJya5DK5w&feature=youtu.be
Quora
https://www.quora.com/How-do-I-integrate-dfrac-3x-3-x-2-2x-4-sqrt-x-2-3x-2-dx
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