Solving MIT Integration Bee Problems (2)

[@awawpogi3036]

why did you put the answer in the title PS: im joking

[@srpenguinbr]

For me, it seems useful to use u equals to the argument of function, if it is not a simple x

[@nathanielsharabi]

brillent idea! im gonna remember to look out for something like this next time a integral looks suspicious

[@LetsSolveMathProblems]

Yes, hints like (pi/2)^2 often signal potential steps to take when evaluating an integral. =)

[@chl5579]

This integral can be use smart formula, that not only just one step only but also give up u-dv format, DI method.

[@amritbahl1223]

Hit like if u solved this problem in one go

[@kamehamehaDdragon]

I love your videos man! I have one question, why in the substitution its sin u, instead of sin u^2, if you used the derivative of u^2 to replace dx? Thanks in advance. Keep it up dude!

[@LetsSolveMathProblems]

Thank you so much, DoobieDui, for your compliment! I truly appreciate it. For the substitution, realize that we are letting u=sqrt(x), so we replace sin(sqrt(x)) with its substitution equivalent sin(u); what we differentiate to replace dx is independent of what we should do to change the integrand (that is, the function inside the integral). In other words, we calculate the new function and new dx separately. Hopefully this helps! =)

[@kamehamehaDdragon]

Thanks, it does help a lot, I think I get integrals a little better now. Also that makes integrating much more fun.

[@burry218]

Awesome work.

[@awanitranjan9730]

Veeerrrry simple q

[@markgross9582]

That’s a stupidly easy integral, isn’t it?

[@omarbahena996]

To get to this level of mathematics what books should one read and/or websites to look for? I mean teachers are a great source, however, their style of teaching may not always be understandable.

[@nobivy3524]

try differential calculus and then integral calculus or calc 1-2. however, integrating can get quite difficult and is a whole other field. so integration is mostly just practice rather than the learning of materials

[@lalitverma5818]

Easy question

[@rot6015]

Nice, got it right :)

[@AlexVasiluta]

What does someone say to a person that wants to conquer the (math) world?

[@marcushendriksen8415]

You dee you?

[@rajthomas4224]

What is the math class requirement for MIT Integration Bee? I am in calc 2 I am able to understand this and kind of solve it out.

[@hogridaaaa6369]

Yea calculus 2 should be enough, but this is very simple problem, but I recommend the the book Inside Interesting Integrals book for practice. MIT integration bee is very hard, not because you cant solve it, but people do it really fast in the competition, and to get as fast as them, you need to memorize as many integrals as you can, also know u substitution, integrals of powers and all trig functions, integration by parts, partial fractions, trig substitutions, completing the square, elimination of radicals by substitution, substituting the tangent of half angle, integrals of hyperbolic functions. In addition, you need to know all the double half angle formulas, and be able to do partial fractions in your head. If you can do all this, and have very fast mental math skills, then you should be ready to go. Mainly, practice Inside Interesting Integrals book, and mit integration problems as well.

[@rajthomas4224]

@@hogridaaaa6369 thank-you, I will take some time into this.

[@hogridaaaa6369]

@@rajthomas4224 Are you studying at MIT right now or are you in highschool, and planning to go to MIT. If you are applying for universities as a senior right now, there are many universities that also have integration bee, and MIT integration bee is arguably the hardest of all the universities that have integration bee.

[@pritamsaha2947]

How π×π/4 turns to π/2???,plz reply!!

[@didodido103]

Look again, he wrote Pi*Pi/4====(Pi/2)^2

[@mokoufujiwara1281]

In the middle there is clearly a mistake that you have written u as x.

[@douglaslee6731]

Nice video bro

[@LetsSolveMathProblems]

Thanks, Douglas Lee! I appreciate it.

[@mikeljanhajrullaj5784]

And the integrale of sqrt[sinsqrt(x)] ?! ...

[@philipphoehn3883]

non elementary

[@stewartzayat7526]

@@philipphoehn3883 how did you know that?

[@mokoufujiwara1281]

I feel that you were drunk, or too tired when recording this video. Have a rest!

[@disharahettiarachchi315]

Can you do tan((x)^1/2) ??

[@sarveshkumarjain7015]

Even I was able to do

[@vineetshady1867]

This is a basic 12 grade maths problem in india ....

[@adenpower249]

It probably is in all countries. The integration bee is difficult because of how fast the participants are.

[@marioguercio5440]

En esta sencilla integral, se puede observar lo mal que explicas. Estamos en 2020, espero haya mejorado.

[@abbaskagdi1]

2 + pi should be the answer

[@sagov9]

why do you think so? btw to be sure i checked it with matlab, and it agrees that the answer is 2

[@Kcgrade095]

no it shouldn't, it's 2