Integral of floor function

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Prime Newtons

5 ай бұрын

In this video , I showed how to integrate a floor function

Пікірлер: 58

@ernestdecsi5913 4 ай бұрын

I'm retired from Slovakia and I love the mathematical examples posted on youtube. I find this valuable, I have never solved such an integrated one.

@Moj94 4 ай бұрын

It's the ceiling. Basically.

@fahimahamed4648 4 ай бұрын

Your voice is great and your teaching is so great ❤❤❤

@soul__nilesh..3821 4 ай бұрын

You are great sir 🎉

@samuelpaulitos4059 4 ай бұрын

I have never heard of the floor function before in my math classes. It's something new I learned in this area. You explained very clearly to me, with great examples. Keep on going.

@PrimeNewtons 4 ай бұрын

Glad it was helpful!

@YehorKharlamov 4 ай бұрын

I've seen it back in school, but our teacher never explained what it was, since it wouldn't be on exams

@s.gsaiphilip8813 Ай бұрын

When I watch your videos.. I get so interested in MATHS.. Thank you for your valuable contributions..

@gastonsolaril.237 4 ай бұрын

Floor function is very important in data science and quant development (algo-trading). Veeeeeeery important!! Thanks again bro. From the various MathTubers that I follow, you've become my personal favorite during these last few months. You're in the level of the best of the best!

@christoskettenis880 4 ай бұрын

Very good explanation mate!

@jkomis 4 ай бұрын

Great explanation!

@JourneyThroughMath 4 ай бұрын

Thank you sir! I have tackled definite integrals using geometry (not calculus) before. Never have I tackled an indefinite integral using those techniques. I wondered if we were going to use the piecewise definition of the floor function to solve.

@Mehrdad_Basiry-fj4rl 4 ай бұрын

Thanks alot... learn alot...❤❤❤. And if it's possible,make a video for ceil function too...the integral of ceil function...

@PrimeNewtons 4 ай бұрын

Will upload soon

@Mehrdad_Basiry-fj4rl 4 ай бұрын

@@PrimeNewtons thanks...❤️❤️❤️.

@X00000370 4 ай бұрын

Nice job...

@septleo3522 4 ай бұрын

Very nice one!

@ReyazulislamReayal 4 ай бұрын

Thanks for this video

@Danaelivs 16 күн бұрын

POV:it’s 2am, and you like math

@dituluiza1097 4 ай бұрын

Loved that. Ceiling and floor were not in my math vocabulary.

@surendrakverma555 3 ай бұрын

Very good. Thanks Sir

@wagnerperlino5048 4 ай бұрын

Nice job. For me, it is easier to see that we have the areas 1+2+3+4+... minus the half the upper square (triangle) with area 1/2, if we compare with f(x)=x. Then we have to sum them up.

@vp_arth 4 ай бұрын

It is just y=x triangle (x*x/2) with n small triangles (0.5) substracted. So S(floor(x)) = x^2/2 - x/2

@mdabdullahalzabir 4 ай бұрын

Thanks

@dengankunghacharles1115 4 ай бұрын

Well done sir 🎉🎉🎉🎉. ( What about the ceiling function)

@SakshamMahajanB 4 ай бұрын

Have done a lot of questions like this while preparing for jee

@raja2850 4 ай бұрын

Where was floor function

@raja2850 4 ай бұрын

GIF is what I saw

@SakshamMahajanB 4 ай бұрын

@@raja2850 Bhai ji usko hi floor function kehte hai 😃

@raja2850 4 ай бұрын

@@SakshamMahajanB Aaj pehli baar floor suna 😁

@wira2562 4 ай бұрын

Like a ladder function, sir

@newperve 4 ай бұрын

So the integral of the ceiling function would be the integral of the floor function plus the number of integers because the ceiling function is the floor function plus 1 except where x = an exact integer.

@tanmayray2326 4 ай бұрын

it'll be more simple: sum of all integers from the lower limit( here 1) to just less than the upper limit(here 5) so it's sum of 1 to 4 & it's 10

@vgautamkrishna5197 4 ай бұрын

got a general formula int(a,b)floor(x)=na+{n(n-1)/2} where a and b are positive integers and b=a+n

@justabunga1 4 ай бұрын

How do you prove that the integral of floor(x) is (x^2-x)/2+C? For some reason, when I looked up through Wolfram Alpha and Symbolab, it doesn't have in terms of standard mathematical functions. I don't see where it's coming from.

@malte3756 4 ай бұрын

this only works for integer x, I'm pretty sure. Easy way to see that is that within each step of the staircase, the area should increase linearly, not with x²

@richardbraakman7469 4 ай бұрын

Does this still work if the bounds of the integral are not integers?

@nothingbutmathproofs7150 4 ай бұрын

Absolutely, just understand that the beginning and end bases won't be equal to 1

@IsomerSoma 3 ай бұрын

Almost, but the adaption you have to make is pretty obvious. You calculate up to the the floor of the upper bound (=n) with the gaussian formular and then add width*n, where the width is the difference between the upper bound and the floor. You can generalize this also with a real lower bound which is just as straight forward. Another note: this is actually a way less weird integral than it seems as in fact the integral is constructed over "simple functions" and the floor function is an example of such a function.

@sudiptoatutube 4 ай бұрын

The floor function should have been called 'staircase' function, because that it how it behaves! 😀

@markfornefeld299 4 ай бұрын

The next video should be about the ceiling function

@psionic0 4 ай бұрын

So (x(x + 1))/2 would actually be the ceiling, right?

@chaosredefined3834 3 ай бұрын

So... Problem. Suppose I want to integrate floor(x) dx from 1 to 1.5. Well, that's super easy, as it's equal to 1 everywhere in that range. So, it's 0.5. Now, let's use your magic formula. It's (x^2 - x)/2 evaluated at 1.5, then same evaluated at 1, and we take the difference. Well, plugging in x = 1, we get 0. Plugging in x = 1.5, we get (2.25 - 1.5)/2 = 0.75/2 = 0.375. So, we get the integral evaluating to 0.375. So... 0.375 = 0.5. Either your magic formula is busted, or math is broken. The secret is, your formula is busted whenever one of the end points isn't an integer. To fix it, try the following: The integral of floor(x) dx = floor(x) ( floor(x) - 1 ) / 2 + floor(x)(x - floor(x)) + c.

@noreldenzenky1527 4 ай бұрын

Sir How we get the area under a discontinuos function ?

@Th3OneWhoWaits 4 ай бұрын

In the very last step, is it the integral of x dx or integral of the floor of x dx?

@mihasdrazdou 4 ай бұрын

Does this formula works only when integral interval is integers?

@PrimeNewtons 4 ай бұрын

I think it works for all real x. Remember, you can cat the Rectangles to tiny straps not just 1

@mihasdrazdou 4 ай бұрын

@@PrimeNewtons will arifmetic sequence work after that strap? I don't think so

@PrimeNewtons 4 ай бұрын

I may need to think about it.

@Luwi1996 4 ай бұрын

@@PrimeNewtonswhat about when you integrate from 0.5 to 1. The area should be 0, but the formula gives (1²-1)/2 - (0.5²-0.5)/2 = 0.125. Or did I do something wrong there?