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The last one is beutiful

for the second question we dont need to substitute we can just do sinx/ cos^2x = sec x . tan x and then integrate so the answer will be sec x which is the same as 1/ cos x

I loved this video, amazing animation and easy to follow.

Indian board contain same type of questions

As a normal Indian student in class 12 It seems easy and I was able to solve all these

Great! Recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023" You can simply find it!

Well explained

7:00 I think the integral becomes faster if you let u be sin 100x and v be sin^100 x. It follows that the integrand is just the derivative of uv divided by 100 and by fundamental theorem of calculus, the answer is easy to see. How would you know to do that? Pattern recognition. Also, I've noticed that sums on the bee tend to be derivatives of products in disguise. The real ingenious part is understanding that you need to split the sin(100x) into a sum.

In 2nd question u can write sinx/cos^2x to tanxsecx with Is integration of secx 👍 Do not let u = cosx 👎

Mmm. No. That logic in the first minute and thus baseless mathematical assumptions following from it is so backward and flawed, I can't believe it is being taught. The reasoning is that Energy is not conserved because the universe expanded and the universe expanded because we assume, due to Einsteinian math, that energy must not be conserved. Edwin Hubble never concluded his observations signified expansion and he warned explicitly against that simplified interpretation of wavelength change which knows many causes. The reification of Einstein's mathematical equation leads to undue complication in the form of extra assumptions. The Emmy Noether idea was used to try to save the day by saying that ‘if not everything is conserved, some things can still be assumed to be, here is an equation for it’, although she phrases it in a more complicated mathematical manner. All this because of the faulty and disproven assumption of the Lorentz transform in Einsteinian relativity. The observation of the existence of Einstein rings, whose lack of a tapering off behavior does not follow the predictions of Einstein, but were already a prediction of Classical mechanics, disproves the assumption underlying the Lorenz transform. If places and matter in space can bend light, which they can due to difficult to reliably quantify distant density gradients, and annulling effects, we cannot reliably use light to say anything about distance and velocity because that would only introduce extra assumptions (or the introduction of calibrations, which are guesses). Hence it undermines any basis for Einstein's relativity logic that depends on the former to be true. You have to start from the recognition that the universe is lumpy, and so is all of space filled with density gradients. Measuring speed cannot be done reliably. Hence we cannot reliably compare distant reference frames. Einstein's relativity can simply not work. Because of the density gradients, what we can reliably know is limited to our direct surroundings. Because we cannot reliably say what is farther away and cannot exclude its influence on our local area, all local systems have to be assumed to be open. Either as a sink or source for energy. Hence, neither the idea that energy is conserved nor the idea that energy is non-conserved are correct. Because all locally observable systems have to be evaluated with regards to the intensity of their in and outflow. This would also makes sense of Hubble's ideas in another way: in our local open system we measure an expansion, our locality being an outflow, hence a source; but elsewhere in the universe, there might be a sink. The extrapolation however that the universe, beyond the observable boundary, must also be the product of the same singular event called a Big Bang, cannot be reliably made.. On the level of the Universe we cannot reliably conclude whether energy is conserved or not conserved. Conclusion: A New Physics has to start from the idea that all local systems are open regardless of any theories about conservation of energy which are just approximations and always wrong when measured at a finer scale, accounting for the in- and outflow into the system.

Don’t get dumbing this down by putting completely unnecessary and distracting music over the narration. 👎🤷🏼‍♀️

Gracias.😊👍🏼

This is the best explanation I've come across, finally I get it! It seems like teaching magnetism years before relativity and calc 3 causes a lot of misunderstandings. I've shared this playlist with my physics class. Thank you for making this series!

For integral 2 you can also do the substitution x = pi/2 -u, it becomes 1 +cosu = 2(cos(u/2))^2 Then we have integral of secant squared which is doable since its equal to tangent

These are question form NCERT in 12th class for Indian people these are nothing compared to jee advanced questions 😂... btw nice video 👍♥️

I think a single charge has flux but no field around it. Electric flux is a scalar qty. measured by its density. Electric field which is a force field appears only when electric flux of one charge interacts with flux of other charge. Both, electric flux density and electric field strength follow inverse square law.

Animations are superb!

For the 2nd question, where did the bounds of integration come from ?? They werent there in the 1st place

Excellent video however the Sagnac Effect and experiments provided differences in light propagation supporting the induction of light through a medium.

Böyle matematik mi çözülür.slayt gösterisi gibi.cografya dersi mi bu.hangi işlemi yaptığınız belli değil.sacma sapan bi slayt gösterisi olmuş

im in year 9 and i watched this whole thing having no clue what was going on but it looked cool

I’d love to see more maths / science videos!

greeat vid

Hey! Great content! Which app are you using for the animations?

Hi Colin. If when moving the proton is repulsed, why is it not attracted when stationary? Surely in the stationary reference frame the electrons are closer together?

Moreover, perpetual motion machines are possible and thermodynamics laws can be violated

Stupid question : where do the bounds of the integrals come from ? They don't appear until you solve those integrals in the end...

Let's graph f(x). As you can see, its just a triangle. Yeah, of course i see :D

Just use t = tan(x/2) for the second question. For the 3rd question Integrating by parts is so easy, you get (x)(arcsin(cosx)) + (x^2)/2 + C. Anyways nice video!

So is it possible the the energy of matter and charges is dependent on time in such a way that makes the total energy of the universe independent of time?

3:13, how about just write sinx/cos^2x as tanxsecx, and then integrate tanxsecx= secx? I’m sure that is faster than u substitution right?

Nice animations, really enjoyed the video

Third one is an indefinite integral

You didn't show the steps at the last integral where integration by parts was performed.

Being a JEE aspirant, I was able to solve four of them with my syllabus .......... So is JEE difficult or is MIT's integration bee consists easy question ??????

Wait how is the first one challenging.....

Excellent content

Fuck man! These are very basic questions taught at class 11th and 12( equivalent to somophore) and JEE Advanced level in India.

Really awesome series! do more qed

You said you watched several of those, which ones are available? And links? (I've watched the 2015 one)

Hey great videos! Would be willing to share your code?

Which software do you use for animating the algebra operations?

A physics themed channel with the aesthetics of 3Blue1Brown? Suscribed

Nice! is e the permittivity of free space?

Great video! but if you can; could you try and improve the audio?

Great video! Keep it coming!

The third one was nice

is this for the breakthrough junior challenge?

Great video.

Really cool, please continue.