วีดีโอ

how did you learn how to integrate these kinds of functions like the ones in the MIT integration bee? I would love to learn this stuff!! Do you have a discord where we can talk?

yknow i really wish ginger maths friend was in this

40 minutes of pure ginger math! we are so lucky

Black holes were popularized by television and movies beginning in the 1960's. Einstein repeatedly said that they cannot exist. He wrote in 1939 - "The essential result of this investigation is a clear understanding as to why the Schwarzchild singularities (Schwarzchild was the first to raise the issue of General Relativity predicting singularities) do not exist in physical reality. Although the theory given here treats only clusters (star) whose particles move along circular paths it does seem to be subject to reasonable doubt that more general cases will have analogous results. And this is due to the fact that otherwise the constituting particles would reach the velocity of light". He was referring to dilation. It's the phenomenon our high school teachers were talking about when they said "mass becomes infinite at the speed of light". This doesn't mean mass increases, it means mass becomes spread throughout spacetime relative to an outside observer. Time dilation is just one aspect of dilation. Even mass that exists at 75% light speed is partially dilated. It occurs wherever there is an astronomical quantity of mass. This includes the centers of very high mass stars and the overwhelming majority of galaxy centers. The mass at the center of our own galaxy is dilated. This means that there is no valid XYZ coordinate we can attribute to it, you can't point your finger at something that is smeared through spacetime. In other words that mass is all around us. Sound familiar? This is the explanation for dark matter/galaxy rotation curves. The "missing mass" is dilated mass. Dilation does not occur in galaxies with low mass centers because they do not have enough mass to achieve relativistic velocities. It has been confirmed in 6 ultra diffuse galaxies including NGC 1052-DF2 and DF4 to have no dark matter. In other words they have normal rotation rates.

did u know g=9.81

i saw it first

Thank you for this video. If you would like to calculate the x value corresponding to a 95% confidence interval with df > 2, how can you apply the approximate function? It will be exciting if I can watch an example in your new video!

🌲🌳 log

freaky sonic video next

ur bald fans (me) were anxiously awaiting this video

One can make life simpler by choosing b as the Feynman parameter. dI/db = 2b \int^{\infty}_{-\infty} dx i/(x^2+a^2)(x^2+b^2) = 2\pi /a 1/(b+a) by contour integration. Then I =( 2\pi/a )ln(b+a) + c. Setting b=0, we get J=\int^{\infty}_{-\infty} dx ln(x^2)/(x^2+a^2) = (2/pi /a )ln a . Thus, c = 0. So, I = ( 2\pi/a )ln(b+a).

zesty

can you explain eulers identity

integrating for funsies?

ginger math biology takeover when?

this is so neat i love it when people do math neat

I think I’m in the wrong classroom

You ate and left no crumbs

ginger what about cultural ecosystem services :(

deforestation bad :( tree good :)

love this man

Imagine taking APES

I can barely hear you

hi! i'm so so confused, do you mind explaining the concept of squircles for a beginner in math to then explain deriving the volume formula. please😭

ceil(x)-x=1-{x} 0<={x}<1, so the geometric series for 1/(1-{x}) converges. The problem, then, is finding the ceiling of the sum, because if {x} is something like .999 the ceiling will be much higher than when it's something smaller like .6

ISABELLA GOT A LOLLIPOP!!!!!!

I understand every bit of this!

I always thought those floors and ceilings were so hard.

Nice video! Are you not forgetting a (-1)^m in the final solution due to the i^2m?

Hi 🙂Maybe at 16:41 you should add (-1)^m

4:45 Missed a t multiplying the second log.

wow the mic quality is so good

Looks interesting, but I can't figure out what steps you're skipping when you claim an bounds of zero and two for the integral wrt t.

specific heat of potato is about 3.4 kJ/kg

Here’s to hoping you continue this series

Nice one

Very interesting

WOAH!!! 🤯🤯🤯🤯

I've used f(z) = ln(z + ib) / (z² + a²) , b>0 And then contour integration by using upper side rectangular contour with residue at z = ia , and then equating real parts and we got it.

Integration by parts twice and substitution x = tan(t) leads us to the integral -4\int_{0}^{\frac{\pi}{2}}\ln{(cos{(t)})}dt

I'm curious to know how we can the pole at z=i because it is of infinite order and the power series can't be used as well due to the 1/(z+i) being there...any ideas on how to calculate it...?

I=int[-♾️,♾️]((1+x^2)^-(n+1))dx x=tan(y) dx=sec^2(y)dy I=int[-pi/2,pi/2](sec^(-2n)(y))dy I=2•int[0,pi/2](sin^0(y)cos^2n(y))dy beta(u,v)=2•int[0,pi/2](sin^(2u-1)(y)cos^(2v-1)(y))dy I=beta(1/2,n+1/2) I=sqrt(pi)gamma(n+1/2)/gamma(n+1)

y=x^t x=y^(1/t) dx=1/t•y^(1/t-1)•dy I=1/t^2•int[0,1](ln(y)ln(1-y)/y)dy u=ln(y) dv=ln(1-y)/y du=dy/y v=-Li_2(y) I=1/t^2•(-ln(y)Li_2(y)|[0,1]+int[0,1](Li_2(y)/y)dy) I=Li_3(1)/t^2 Li_3(1)=sum[k=1,♾️](1^k/k^3)=zeta(3) I=zeta(3)/t^2

what about the arcs tho?

I didn't use complex analysis but simple integration techniques and I got the result Integral(-½ to +½) Γ(1+x) Γ(1-x) dx = (4/π) β(2) = 4G/π Here β is dirichlet beta function.

Please dont say lohopitals)

Choise of contours always seems completely arbitrary to me ://

bro forgot to edit out the first take