Funny math problem to calculate the Pin Number for a credit card.

08122021, 03:05 PM
(This post was last modified: 08122021 03:52 PM by Albert Chan.)
Post: #6




RE: Funny math problem to calculate the Pin Number for a credit card.
(08112021 03:40 PM)Albert Chan Wrote: I2 = ∫(1/√(x^23x+2), x=0..1) // let y = 2*(x3/2)=2x3, dy = 2 dx Another way is to map y=2*x3 for the full integral, then solve by integration by parts Note that above quoted expression, map from x to y, numerator of 1 stayed 1. XCAS> e2r(r2e([3,1,2,4], (y+3)/2), y) → [3/8, 25/8, 77/8, 55/8] I = ∫((3y^3 + 25y^2 + 77y + 55) / √(y^21), y=3 .. 1) / 8 Y0 = ∫(1/√(y^21),y) = ln(abs(y+√(y^21))) Y1 = ∫(y/√(y^21),y) = ∫d(√(y^21)) = √(y^21) Y2 = ∫(y^2/√(y^21),y) = ∫(y*d(Y1)) = y*Y1  (Y2Y0) 2*Y2 = y*Y1 + Y0 Y3 = ∫(y^3/√(y^21),y) = ∫(y^2*d(Y1)) = y^2*Y1  2*(Y3Y1) 3*Y3 = (y^2+2)*Y1 3*Y3 + 25*Y2 + 77*Y1 + 55*Y0 = (y^2+2)*Y1 + 25/2*(y*Y1+Y0) + 77*Y1 + 55*Y0 = (y^2+25/2*y+79)*Y1 + 135/2*Y0 I = preval((y^2+25/2*y+79)*√(y^21) + 135/2*(ln(abs(y+√(y^21)))), 3, 1, y) / 8 = 101/8*√(2) + 135/16*ln(2*√(2)+3) ≈ 2.98126694401 

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