Integrating Floor Functions is Simple

[@txikitofandango]

Great problem and solution! Not sure if all that stuff at the beginning is necessary. It's easy to show with a derivative that the function inside the floor brackets (let's call it f) is strictly increasing over the interval (0,10). Especially considering that the square root of an increasing function is also increasing. Then, f(0) = 0 and 3 < f(10) < 4. This tells you all the points you need to solve for. It makes sense when you see it graphically as the sum of the areas of 4 rectangles (including 1 degenerate rectangle). The heights of the rectangles are 0, 1, 2, and 3, and their respective widths are (1/9 - 0), (2/3 - 1/9), (9 - 2/3), and (10 - 9).

[@cantcommute]

you can show it's strictly increasing by the way he wrote the integrand squared in the video (as 10-10/(x+1)) which is even quicker

[@3ternalHours]

Really didn't expect him to solve this through brute force...

[@jrckhome4799]

What are the other ways?

[@ieee12345]

@@jrckhome4799 You set u = (stuff inside the floor), do the substitution, then the floor function splits trivially in the sum as its argument is just the integration variable.

[@cantcommute]

i solved for x in the cases the integrand squared is 0,1,4,9 and noting that the function is strictly increasing (because integrand = 10-10/x+1

[@jarikosonen4079]

It looks clear, but should it be shown that value is 0 at x=0 and up to x=1/9?

[@nickcheng2547]

Since it had been proven that the integrand can be 0,1,2 or 3 only, and that 0

[@AWESOMEEVERYDAY101]

U can take the derivative of the inside of the root and see that's it's always positive

[@NullClass]

Simple question whose only difficulty is to solve quickly. Is this really a good way to test students? Don't know the context, but believe that you can make much better questions - even with basic math.

[@NullClass]

@@MyOneFiftiethOfADollar Why so bitter?

[@NullClass]

@@MyOneFiftiethOfADollar 1) I don't need to have produced anything to be able to critique someone's video. The "then do better" argument is obviously flawed. 2) I'm not even criticizing the video, which clearly is a learning tool. My problem is with the use of questions like this in a uni. selection exam. This seems to be that kind of question that is in the test and is challenging just because of how fast you would need to solve it. And in my opinion this is in no way the best way to test students.

[@NullClass]

@@MyOneFiftiethOfADollar Your efforts in defending a video I didn't even criticize are commendable. Also, props for your absolutely amazing argument that I need to make a video myself in order to criticize this one (again, that I didn't even criticize), which is what I would expect from a 10 y.o . No idea why you are so butthurt, but at this point it's clear you are obstinate. Rest well, my friend. With you I no more shall lose time...

[@nagamanikomarla5376]

@@NullClass I completely agree. This question is from JEE Advanced, which is an entrance examination for engineering colleges in my country. More than ingenuity, the exam tests the ability of the student to solve horrendous looking questions quickly (atleast when it comes to the math section).

[@Maths_3.1415]

​@@nagamanikomarla5376 jee is lol infront of olympiads stupid

[@atikshagarwal2649]

Hey can you take some questions on differential equation

[@andresmartinezcarcel1637]

No, go back to india

[@nicogehren6566]

very nice solution

[@varadramkrishna6314]

This video gonna get lot of views.....

[@m.venkadesen9037]

🤩

[@pradyumnanayak9844]

🙏

[@yoav613]

Simple,it is.

[@ReckonClasses]

👍

[@patrick-8068]

define​ Root(10x/x+1)dx​ take​ log. 10x/x+1*dx(p2) Integate 0+5dx+20dx... Answer

[@Aqua17292]

From which JEE Advanced is this problem??

[@biswakalyanrath966]

2021

[@jimmykitty]

🥺🧡

[@mustafizrahman2822]

pff...............

[@jimmykitty]

@@mustafizrahman2822 kichui bujhi nai vai

[@nirmankhan2134]

I solved it. 🗿

[@mustafizrahman2822]

@@nirmankhan2134 pfffffffffffff

[@mustafizrahman2822]

@@nirmankhan2134 how

[@축복-l1l]

asnwer=1

[@sandhyaraninayak1492]

Directly find area , a naiv 11th student can do that 😂😂😂

[@NoxIITK]

Bhai Not gonna Lie, In this much time, You are gonna skip to the next question and later realize how big fool you were to skip it. We go through it everyday.

[@NoxIITK]

PS: Also you can equate 10x by x+1 to m² and find x in terms of m. It will save time to find integral limits during exam.

[@richardfredlund3802]

@@NoxIITKthat's how i did it 10x/x+1 =m^2 ---> x= m^2/(10-m^2)

[@dr.mikelitoris]

Then just don’t be dumb?

[@NoxIITK]

@@dr.mikelitoris Whut do u mean ? Are You Indian?

[@andresmartinezcarcel1637]

India is greatest countri