Completing the 2020 MIT Integration Bee Qualification Test

[@ezequielhorvitz1610]

Please use a pen, pencil is barely visible.

[@HawkMath]

I will make sure to do this in the future!

[@afrolichesmain777]

This video has a 2013 feel to it. The quality is top notch. You sir, have earned my subscription.

[@Mayank-hm7cc]

Normal school : spelling Bee MIT : Integration bee

[@crinoidgaming9296]

Thats why they are no. 1 university.

[@IGrowKnees]

How do you use a pencil holding it like that?

[@teddahmer3338]

Bro. How can somebody understand this? That's a gift for real.

[@charmelonchannel]

Not really, calculus is a pretty basic topic in math. It only requires computation, which can be mastered with some practice. Serious mathematics though, is much harder and involves serious mind-fuckery

[@gameguy8101]

Take one calculus class and practice a bit, all of this kind of stuff can be done after taking calculus 1 and calculus 2

[@teddahmer3338]

@@charmelonchannel Thank you. For me that looks very serious to me 😅

[@teddahmer3338]

@@gameguy8101 OK thanks.

[@yashrawat9409]

One fun way is to be born in India and study for Jee ,

[@anujgupta5348]

Fun fact you can find most of these question in NCERT of +2

[@yashrawat9409]

Q1. 1/x is d(log(x)) asume it t , open 2x as log2 + logx , standard question Q2. Multiply and divide by e^x and take it t as d(t)d(x) is t , then just 1/t - 1/t+1 Q3. AGAIN 1/X , assume t , apply by parts i guess(I have been out of hand for some properties of definite integration like kings etc.) Q5. denom is 2x² -2x +1 make it 2[( x-1/2)² + (1/2)²] then it's standard procedure 1/a tan-1(x/a) I might be completed wrong about these continued fractions but i think it is equal to x Q7 has multiply divide by 16 , make sin(2x)^4 , other thing is cos(2x) that is 1/2 of d(sin(2x) , substitute and done

[@heeraksharma1224]

For 2nd , multiple and divide by exp(-x)

[@a_llama]

14 was one of the easiest lmao, given that in the 2nd fraction, the numerator sum is the derivative of the denominator sum. Loved how it cancels out with ln|x-1| in the end

[@kingrobert7246]

oh you love that dont you

[@sagargour2024]

No-one Asians: This is too easy 😂😂

[@weronika2541]

I would like to know mathematics like that too

[@harrisonrogers9797]

UTTER GENIUS

[@rayderwiliamleonardolaura5657]

I have a big doubt, ¿Why log(x) is equal to Ln(x)?. Since, the first is a logarithm of base 10 and the other is the natural logarithm. Therefore, they are not the same. My question is about exercise 3

[@takyc7883]

I would liek if I could see what was happening

[@HawkMath]

Sorry about that, I have started using pen in all my new videos and spacing out the questions more

[@user-lm8mi9hy5g]

It would be good for us to do the math with more space

[@jgsh8062]

ikr imagine doing 10 integrals on a single piece of paper

[@cuberkahmin42]

im sorry, can i ask ? Q15 , after you substitution u=pi/2 - x , and you change dx to -du, and how can you change back the du to dx without change the boundary ?

[@zackbach1]

Why can you just rewrite logs as ln?

[@HawkMath]

Idk why, but for the MIT integration bee "log" is assumed to be in base e, so I just write "ln" in my work since that's what I'm used to. This is cleared up in the clarifications. Note, many other places also use this convention, so its always good to check which one is being used.

[@zackbach1]

@@HawkMath Ahh ok. I was unaware that log is assumed to be in base e for the integration bee. Thanks

[@yashrawat9409]

It's almost considered a standard unless specified to take in other base

[@ernestschoenmakers8181]

I do not agree with you on the 6th integral, the integral of sqrt(xsqrt(xsqrt(x........dx, although the answer is correct the way leading to it is not cause this is not the same as: integral of x^((1/2)+(1/4)+(1/6).....dx. The power of x should end up to 1.

[@HawkMath]

What I wrote down on the paper was x^((1/2)+(1/4)+(1/8)+...) which does indeed equal x^1, sorry if this was unclear or the visibility was bad. Another way to solve this is by setting y = √(x√(x√(x...))), so y^2=xy. Then (since y is not 0), y = x. This means that √(x√(x√(x...))) = x.

[@ernestschoenmakers8181]

@@HawkMath Thanks for clearing this.

[@kyuzo3313]

nice video, i like it.

[@ryanwilson9555]

Derivative Error: *log x* ≠ *ln x* d/dx [ *log x* ] ≠ d/dx [ *ln x* ] 1/( *x ln 10* ) ≠ 1/ *x* Given log( *a* , *x* ), where *a* is the base of the logarithm and *x* is the argument, such that *a* > 0 and *a* ≠ {1,e}… d/dx [logBASE( *a* , *x* )] = 1/( *x* ln *a* ) *log x* is base *10* *ln x* is base *e*

[@kbuilds7287]

mit integration bee rules. Logx has a base of e, so log x = lnx

[@progmaster15]

log x is also base e, lg x is base 10

[@ryanwilson9555]

@@progmaster15 I was taught that ln x is always log x with a base of *e* instead of *10*.

[@priyansusingh1272]

Amazing 👍🏻👍🏻👍🏻

[@nicogehren6566]

the issue is great but i couldnt read it

[@gkatoch1982]

Please, use some dark pen and write bigger on a bigger piece of paper, its illegible. Although I like your content.

[@brkkk3754]

Really great but your pencil is the problem

[@HawkMath]

Thanks for the input, I have started using pen now.

[@abhisiktajoarder1116]

This video was wonderful !!!! Although donno why this seems so easy to me(a high school student)😅

[@lucagiovanninieddu2603]

You solve way too fast

[@crinoidgaming9296]

I want the full page

[@HawkMath]

I don't understand what you mean

[@crinoidgaming9296]

I want full question paper through pdf or else, or here is my gmail id [e-mail]

[@crinoidgaming9296]

@@HawkMath i am preparing to create a Guinness world record next year in my summer vacation" most integral" solved in 12 hours .So ,i am preparing for that . I am in 9th now and will go to 10th next year .I am from india. I want to go to IIT .Maths is not my love ,its my addiction and Calculus is my favourite topic.So, pls send whole question through pdf on my mail. And , also i will create record for most differentiation solved in 12 hours in my winter vacation next year.So , I am also preparing for that.

[@HawkMath]

@@crinoidgaming9296 it's at the bottom of the MIT Integration Bee page that's linked in the description

[@crinoidgaming9296]

@@HawkMath thanks

[@harshgandhi7514]

Nice 👍👏

[@thebigfoot4456]

Use a pen not pencil pls

[@HawkMath]

Thanks for the input, I have started using pen now.

[@pokoknyaakuimut001]

😍😍😍

[@Frustrated-swks]

Sir video quality is very low

[@dr.palsonp.h.d815]

Im pretty sure he went through these before the video and is just explaining the solutions, would be nice to see a live run of this with no preperation

[@martini.1999]

why do you think so?

[@dr.palsonp.h.d815]

@@martini.1999 the explanations are rehearsed

[@martini.1999]

@@dr.palsonp.h.d815 how do you exclude the possibility that a person is able to do this off the cuff?

[@dr.palsonp.h.d815]

@@martini.1999 because they are not, if you have ever done anything like this, then you would know that even the most experienced professors have written notes with them during presentations/lectures.

[@martini.1999]

@@dr.palsonp.h.d815 i know for myself that these problems can be hard and sometimes take a lot of notes (im studying physics). but i know that there a people that a far better and faster at solving integrals. and there are also competitions revolving around solving integrals fast. the considerations he makes are pretty standard for a someone for someone who is educated in that field, which is why i think that your assumption is false.

[@josephokosun8342]

Hmmmm

[@user-ll4sr5nl4f]

Too easy~~

[@swipingeverymoment]

This is just a QUALIFICATION TEST