Yes - fun math with a ginger! Mostly all forms of calculus, complex analysis, analytic number theory, and diff eq, with a bit of physics sprinkled on top on Phridays.
i used a quite different method which actually turned out simpler: i used the identity arctan(x)+arctan(1/x)=pi/2, to rewrite the starting integral as pi/2-arctan(1/x) all over x (and all squared), expanding the square we get 3 integrals, 2 of which trivially go to zero (odd functions), and we're left with the integral of arctan(1/x)^2/x^2, and being even i multiplied by 2 and changed the bounds to from 0 to inf i then subbed 1/x=u, which easily simplifies, and with some further calculations you end up with twice the integral from 0 to inf of ln(x^2+1)/(x^2+1), where subbing tan(t)=x transforms the integral into 4 times the integral from 0 to pi/2 of -ln(cost), which is a known integral which evaluates to -pi/2ln2. multiplying with the -4 in front we get 2*pi*ln2
The only way to get a square out of a single parametric equation (that I know of) is to form a square is just to take the limit as n-> inf for the parameterization for a squircle - might just be easier to visualize here: www.desmos.com/calculator/k4majn258z But any integration with squircles is likely bound to be much harder and unnecessarily complex than four integrals around line segments.
@@MeatiusGaming Forgot about the case where n = 1... so yes 😅 - though the parameterization of it would still involve either 4 line segments or the square of trig functions
Thank you! I believe this might be one way they do, however, I would imagine this formula only works for integers because of the negative one term (though I could be mistaken).
Even if a bit of fire got into the container I don't think it would've been a huge deal since sulfuric acid isn't flammable. That being said, however, I wouldn't exactly want to find out sooooo that'll be closed next time :D
As a science enthusiast, it may be safer to wear gloves for experiments such as these that can potentially splash back onto your hands. Or to use a long needled on the syringe to increase the distance from hand to reaction. Very cool, but stay safe out there!
I’ve found in situations like this you’re often better off without gloves unless you have something that will for sure protect you. You don’t want to weld a glove to your skin
I mean for odd n it is soooo I suppose that works... though it's a bit harder to make a video if that's just the answer lol - love the trivial solution but nottttt the best for views
La notazione potrebbe non essere chiara: it is ln^n((1-x)/(x)) rather than ln(((1-x)/(x))^n), that is to say the exponent is being applied to the log and not its argument. I'll try to make that clearer next time.
Where can I send you intresting questions for solving for your upcoming videos ? Do you have email or telegram? Love your videos hope u listen me (your audience)
@@GingerMaththanks Actually my friends know how to do it but I don't And please also teach evaluation of high school integrals using it Like u did in gaussian video.
If the initial condition of the object is released from the angle θ and without initial velocity: a. What is the maximum spring elongation length? b. What is the speed of the object when θ = 0? Also what is the elongation of the spring at that time? How do you find the 2 points above?
Nice to see another approach to this problem! Very good job with the contour integral (be very careful around that essential singularity though…). The problem originally came from a math stackexchange post requesting “hard integrals.”
