you could consider it as integrating 1/2 times, and then you can just use riemann-liouville transform (fractional calculus). although the way in which one would interpret sqrt(dx) changes the solution and overall meaning.
@@namu7841 since the dx isn't under its own square root but instead seems to be attached to the x^2 I think it would make a bit more sense to consider the integral as a simple riemann sum from a to b of (x^3cos(x/2) + 1/2)sqrt(4 - x^2dx) where dx = (b - a) / N and x = a + ndx, so we have lim N - > inf [sum {n = 0 .. N) of ((a + ndx)^3*cos((a + ndx)/2) + 1/2)(sqrt(4 - (a + ndx)^2*(b - a)/N))] which evaluates to positive infinity with a = -2, b = 2
What a speed up using these tricks! But I think that when you see such a wifi password riddle you should guess pi, e and sqrt2 for a start and if it turns out to be wrong start solving the integral.
This is pretty cool but i wonder how much harder would it be if you keep dx inside the square root
you could consider it as integrating 1/2 times, and then you can just use riemann-liouville transform (fractional calculus). although the way in which one would interpret sqrt(dx) changes the solution and overall meaning.
@@namu7841 since the dx isn't under its own square root but instead seems to be attached to the x^2 I think it would make a bit more sense to consider the integral as a simple riemann sum from a to b of (x^3cos(x/2) + 1/2)sqrt(4 - x^2dx) where dx = (b - a) / N and x = a + ndx, so we have
lim N - > inf [sum {n = 0 .. N) of ((a + ndx)^3*cos((a + ndx)/2) + 1/2)(sqrt(4 - (a + ndx)^2*(b - a)/N))]
which evaluates to positive infinity with a = -2, b = 2
Honey wake up, new Laid Back Math just dropped
Hey nice video
Just a suggestion: decrease the opacity because at times it was becoming difficult to see the writing
What a speed up using these tricks! But I think that when you see such a wifi password riddle you should guess pi, e and sqrt2 for a start and if it turns out to be wrong start solving the integral.
Well done!
great, the password is irrational now what? :(
ur mic is too quiet