it is called as king property because it fights integral like a king.

@nachiketsharma4507

3 жыл бұрын

Indeed

@VANTABL4CK

2 жыл бұрын

most kings are lazy and fat and just order people around until the people fight back and execute him

Right after surgery, battling cancer and watching blackpenredpen math videos 😂😂😂 ...btw no worries, my chances are at 85 - 90% and one of two tumors has gone today 💪

@faith3174

5 жыл бұрын

i hope you recover soon. sending you good vibes

@blackpenredpen

5 жыл бұрын

I wish you the best luck. Hope you get well soon! I would like to make you a happy mathematician, too. Please send me an email blackpenredpen@gmail.com and we will go from there.

@LS-Moto

5 жыл бұрын

@@blackpenredpen that you very much guys.... I will email you right now :) I live in Belgium, but I hope that's ok :)

@MuhammadFarhan-dp5ej

5 жыл бұрын

Get well mate

@LS-Moto

5 жыл бұрын

@@MuhammadFarhan-dp5ej thank you. Appreciate these kind words :)

Its called the "King" because virtually any trig function can be demolished using the substitution. This is especially true when within logs or when you have a sin/cos pairing. It is also fairly easy to change the bounds from pi/2 to another range by using the R-alpha method or by symmetry on a graph

@herbie_the_hillbillie_goat

9 ай бұрын

Source?

look, whenever I see a definite integral, especially involving trig, I get nervous.

@icespirit

5 жыл бұрын

and sqrt2 in the exponent :p

@vivekt1899

3 жыл бұрын

I just skip the questions lol😂

It always the most intimidating integrals that have an elegant solution! :)

@blackpenredpen

5 жыл бұрын

Sergio H yup!!

@ianmoseley9910

5 жыл бұрын

Integrals are merely representations of relationships between variables; any intimidation is in your own mind

@sergioh5515

5 жыл бұрын

@@ianmoseley9910 k

@vesna1235

4 жыл бұрын

Lmao nice response

I love maths. This video was so crazy. Especially I+I = 2I

@icespirit

5 жыл бұрын

lol

@kreepi8381

3 жыл бұрын

Lol

I can't wait to surprise my math teacher by using this at the exam

@blackpenredpen

5 жыл бұрын

Stefan Stefi nice!!

@harrabiwassim

3 ай бұрын

mine would give me a zero because "we didn't learn it in class"

It's not nice to say FU 😂😂😂😂😂!!!!

@pgoeds7420

5 жыл бұрын

Felix Ungar disagrees.

@stuartyeo5354

4 жыл бұрын

If you say F of u fast if enough you getting f***ing u, and that's not nice as well.

@enrique097

4 жыл бұрын

Fu miley sairus song

@cuberkam9072

3 жыл бұрын

😂😂

Hi Am shedrach from Nigeria Am perplexed with ya teaching As your channel had become my favourite companion and you my favorite teacher Thanks sire

Maybe the name is derived from the castling move in chess, where the king and a rook switch places?

@z01t4n

5 жыл бұрын

Yeah, I'm pretty sure that's the case.

@croxxx3262

5 жыл бұрын

This seems to be the most correct response! (As well as the most romantic.)

@blackpenredpen

5 жыл бұрын

Wei Ni Hao nice!!

@quocanhnguyenle4952

5 жыл бұрын

Lol, that does make sense!

@ianmoseley9910

4 жыл бұрын

I was assuming it was named after a professor King?

I took two full years of calculus and don't recall ever hearing of the King Property. I've had more math fun watching your vids than I ever did in class.

Absolutely very much important strategy to solve definite integrals. I can assure you that , its my one of the most cherished birthday presents. Thanks Steve. :) :)

Sir. You have a super gift for making maths so easy and fun

I watched your recent video using the king property which brought me to here for the proof of the king property. Amazing how much you have improved over time! You were still a great teacher here, but you are much more comfortable in your most recent videos and your English has definitely improved. Thanks for all the great content!

Happy New Year, mr Chow! If you celebrate this one.

@blackpenredpen

5 жыл бұрын

Thanks!!!

The explanation of this interesting problem can be described in just two words - SIMPLY AWESOME. BPRP - you rock.

To the person battling cancer: many, many prayers for your COMPLETE HEALING. Please keep on watching this brilliant channel! Stay blessed my friend.

I absolutely love your channel!

Very clear explanations of complex problems. Thank you.

Wow, so cool! Thanks blackpenredpen.

I realized this property a few weeks ago while solving a random research integral involving logs, I had no idea it was called the King Property. Good to know 😊. Geometrically, the king property just says that whether you start from the left or the right, the area under f(x) should be the same, so reflect the curve along the vertical axis and push the curve to the right appropriately, and the property jumps at you. It’s less random than it seems. Nice video BPRP! 🙌🏽🕺🏽🎊💯✨🤓

@mahxylim7983

2 жыл бұрын

thanks！

Nice video!! What a beautiful integral!

Oh..my...god, that is brilliant! Thank you so much!!

It's called King Property because it's used only by Kings of integrals 💪

I saw integral from this example on the math forum with polish language One of the guys suggested to use substitution to make interval to be symmetric over zero and then use additive property addition of integrands not intervals After using additive property first integral should be integral of odd function on interval symmetric over zero and second should be easy to evaluate

This Is so beautiful!!!! Thank you!!!!

Happy New Year

After you do the King property can't you just set x = (pi/2) - x Then that tells you that x = pi/4 Or does that only work because 2*I=1

Thank you professor for the lesson

@blackpenredpen

5 жыл бұрын

Makhlouf Benmehiris you're welcome!

すごい、、、日本の高2ですがただの積分公式とその証明にこれほど驚かされるとは… What a great formula!! I'm surprised that I've been surprised at just a formula and proof (I'm sixteen year-old-student in Japan☺️)

Can you do a video on how to calculate the sum of a harmonic series? I’m struggling to find the sum of this sequence 1/2+1/3+...+1/2019 any help please?

@wpbn5613

5 жыл бұрын

Not the nicest answer ever but I think it's ln(2019) + 0.57722 ? 0.57722 is a constant but I don't remember what kind EDIT: it's actually ln(2019) - 0.42278 I think? Bprp should make a video on this, but I do know the formula converges to "ln (x) plus 0.577" for big numbers

@DragonKidPlaysMC

5 жыл бұрын

It’s actually called the euler-masecheroni constant. How did you come up with the adjusted value of it for lower values of n?

@mat1305h

5 жыл бұрын

​ DragonKidPlaysMC You can either say that sum_{n=1}^{2019} 1/n = integral_{x=1}^{2019} 1/x dx + O(1) = log(2019) + a constant. The constant depends on 2019 and by definition tends to gamma, the Euler-Mascheroni constant, but the convergence is extremely slow (as you'd expect from a logarithmic convergence). Indeed, for n up to 100 000, there is still a mistake at the 4th decimal of the approximation! You therefore can't reasonably expect a good approximation from values of n this low. You could use Abel's summation formula to derive an exact form. Complete the integral of floor(x)/x^2 dx from 1 to infinity to get 1-gamma (see wiki for the integral forms).

@dolphinlunggrin6594

5 жыл бұрын

There is no nice result for this. Since you start at 1/2 what you get is 1 less than the 2019th harmonic number H_2019. There is a formula for those but it's not really helpful. H_n = M+D(n+1) Where M is the Euler-Mascheroni constant and D the digamma Function. So your sum would be M+D(2020)-1 Which is about 7.187820910...

@Cashman9111

5 жыл бұрын

just bring everything to common denominator, easy

youre a funny dude earned my like today.

If you really want to confuse someone who has not seen this before you could use the i'th root of tan(x)

BPRP, I have kind of a burning math question that has been on my mind for almost a year now, but I've struggled to find good explanations for it online. Basically, I would like to know if there is an easy way to find the equations for some parametric curve (say {x(t),x^2(t)}) where the speed (independent of direction) of a particle on said curve must be constant. I have tried setting up the relationship where sqrt(x'(t)^2+y'(t)^2)=1, but I haven't gotten much farther. An explanation for how one could do this, or whether it can be done would be greatly appreciated, even if there is a simple answer.

lol, I got a Kingsford ad in the process of watching this video.

I am touched.

Thank you soooo much

When you did the previous Putnam integral, after you put the substitution x = tan theta if you would have applied king rule the integral would have been much shorter

@nanigopalsaha2408

4 жыл бұрын

Can you please elaborate?

Thank you sir!

I love the line about using f of u instead of f U

It's amazing! It is to solve an integral indirectly!

Very nice indeed!

What a clever technique!

This is the first putnam integral that I did in my head. I am proud of myself :)

Amazing!

Amazing👍👍👍👍

These type of questions (on king's property) are taken in beginner level integration classes in India for students preparing for JEE. P.S.: Queen's property: Definite integral of f(x) w.r.t to x from 0 to 2a equals [definite integral of f(x) w.r.t x from 0 to a]+[definite integral of f(2a-x) w.r.t x from 0 to a], where a is a real number, & this can be proved by writing definite integral of f(x) w.r.t x from 0 to 2a as the sum of definite integral of f(x) w.r.t x from 0 to a & definite integral of f(x) w.r.t x from a to 2a, & then substituting x=2a-t in the definite integral of f(x) w.r.t x, where the upper and the lower limits of x are 2a & a respectively, i.e., the second integral of the sum. In addition to that replace dx by (-dt) and you'll get the desired result, or rather I should say, that's a good place to stop (Michael Penn ref. people😊)! Also, my teacher told our class that queen's is generally used with king's property & even though I've no idea where does king's property gets it's name from, I'm sure the name of queen's property is such due to it's usage with king's!!

@maverickgames5972

2 жыл бұрын

Same here in Hong Kong, it is a primary method for us in the HKDSE Mathematics Module 2 Algebra and Calculus, that we are required to derive the King's property out during the exam and apply it

how do you know what i am studying right now ??? 我感到震惊！

Im Japanese and I just started studying English but I could understand this property easily! thank you!

Good stuff

1/(1+tan^2½x) =sin^2½x/(sin^2½x+cos^2½x) we use the property ..f(x)/f(x)+f(a+b-x)[integration from a to b]=b-a/2 get the value is π/4 as cos x =sin(π/2-x)

Very nice property!

What a creative solution, another one for the bag of secret tricks.

amazing

thanks a lot

@silentintegrals9104

2 жыл бұрын

Totally agree!!!

I just calculated the area under the curve, and it came out to be π/4.

very cool!!

Plz make videos on complex analysis

awesome!

And here comes the king!

@nicholasleclerc1583

5 жыл бұрын

Soumya Chandrakar You mean.... The Qin ? Oh, wait, he already did it at 11:14; nvm...

"it's not nice, say f of u" 😂😂😂 love your sense of humor

can you always call an integral I and then adding and subtracting them?

Hi, may I ask how to integrate this if the upper limit of the integral is pi? A whole pi. Thank you.

I am in strong belief that f (u) is indeed not polite to say, however, love u is! So, I wanted to say: I just called, to say, I love you (bprp)!!

@blackpenredpen

5 жыл бұрын

Svetozar Delchev thank you!!!

@CrystalClearMaths

4 жыл бұрын

It is much nicer to say 10q :-)

Here’s an integral you might want to try solving ((1-u)/u)^x du from 0 to 1. It has a definite value when -1>x>1. The solution can be written in terms of elementary functions. Good luck!

@lucashoffses9019

5 жыл бұрын

star dust I’m curious to know how you got that answer. Did you look it up?

In our syllabus my teachers told that as this property is the most useful one so we call it the kings property and if the lower limit becomes 0 then it is called queens property 🤔🤔

why did you not tell me this one day before I had my maths exam yesterday.

@blackpenredpen can i also ask my doubt ..? If yes then where and how?

Bro I really like your videos.... But only problem is ur videos are very long...... (I watch ur video in 2× speed) to save time. ...

That’s awesome

Hmm. I'm thinking about switching sqrt(2) to y and then writing this integral as function of y. It's constant so its derivative is 0. Then I'd try to get another equality by derivating function under integral over y. Ofc it needs to be proved that it's valid method but it should be doable and maybe it's gonna lead to something interesting? I'll give it a try when I have more time. It was probably done by someone cause if it's famous (though I probably didn't remember this one during my studies as I'm forgetful) then I'm sure someone did that as it seems natural way to get new equalities that may be useful somewhere. I wonder if you can do same trick with half-derivatives as I don't know if you can move half-derivatives under integral. Actually this makes me want to find out more about half-derivatives. ;)

You have a continuity issue since there is an asymptote at pi/2.

Hey everybody, for my Honors English IV class we have to write a research paper on a modern theory in the field we want to study in college. I am planning on majoring in math but I dont have any ideas for topics. It has to be something I can understand enough to write 25 pages about, keep in mind I only have up until trigonometry (I'm in it right now) under my belt. Does anyone have any suggestions?

@blackpenredpen

5 жыл бұрын

I just set up a forum on my site blackpenredpen.com I think it's better for you to post this there since it's kinda hard to others to see this comment.

@angelmendez-rivera351

5 жыл бұрын

Try using hyperbolic functions and relating them to the trigonometric functions.

Hey would you finding the area between the intersection of 2 parabolas of equation of y=x^2 and y^2=x

@faith3174

5 жыл бұрын

to get the area between the curves, y²=x can be written as y = √x (taking the positive branch) now notice that the intersection points of y = x² and y = √x are 0 and 1. in this interval, √x ≥ x² so the area will be area bounded but √x - area bounded by x² ʃ (√x - x²) dx from 0 to 1 will be the area you're looking for which comes out to 2/3 - 1/3 = 1/3

@rumasaha3236

5 жыл бұрын

@@faith3174 thanks for solving my problem

No matter the power tangent is raised to, the answer is pi/4, neat

@blackpenredpen

5 жыл бұрын

Jared Middle yup!!!

Can you prove in a straight triangle when only the sides are divided by 5 then the height to the rest is an integer? I succedded :) . Example- Stand-3 x Stand-4x Over-5x Height -2.4 x Or S-75 s-100 o-125 H-60

This is analogous to a trick you can do with finite sums: Sum from n = a to b of f(n) = Sum from n = a to b of f(a + b - n) It's easy to see why this works if you write it out: f(a) + f(a+1) + ... + f(b -1) + f(b) = f(b) + f(b -1) + ... + f(a+1) + f(a) You can actually prove the integral identity by applying this trick to the Riemann sums :)

I feel like the answer is super obvious, but there's also a chance it's just some calc identity I never learnt, but why does it equal 1 at 9.30? It's super late at night and looking at it makes my head hurt and I can't figure out what the process is . Maybe in the morning I'll have an idea of what's going on but yeah, anyone able to explain?

@weenrar

5 жыл бұрын

If two separate integrals have the same bounds of integration, you can add them together to make a single integral with both expressions on the inside. BPRP added both integrals together, giving him a single integral from 0 to pi/2. So, 1+(tanx)^sqrt(2) on the top, and 1+(tanx)^sqrt(2) on the bottom. Since they’re the same, you just simplify to 1/1 = 1.

Almost i would ask that what if we change the squareroot of 2 after that you said that doesnt matter thanks but why mmm

Can you find a function that apply the relation dervitave(f)=invesrse(f) (First dervitave)

@angelmendez-rivera351

5 жыл бұрын

Scorpion56 Dr. Peyam already made a video on this.

@blackpenredpen

5 жыл бұрын

Peyam did that already.

Your face reminds me of my friend

Let's solve math problems also did a video on this

What module do you dwell into intergration like this? Im a second year in my bachelors and in all the calc classes ive never seen clevel results like this, we only look at different methods? Is this a masters/post grad class?

@angelmendez-rivera351

5 жыл бұрын

gerard No, this is just your regular old calculus

@LYNXzTwist

5 жыл бұрын

@@angelmendez-rivera351 true, they never taught us these tricks they arise in trigonometric identities

@angelmendez-rivera351

5 жыл бұрын

gerard They never taught you that cot(x) = tan(π/2 - χ) ? But that is a basic identity! Your institution must have been sloppy

@LYNXzTwist

5 жыл бұрын

@@angelmendez-rivera351 sloppy is an understatement, but yeah i can instantly see that your dividing through sinx=cos(pi/2-x), which yes at least we were taught that😂

@LYNXzTwist

5 жыл бұрын

@@angelmendez-rivera351 my college got put in. The top 20 worst colleges, my teacher was brilliant but he was an a engineering bachelors not a mathematician

can you do integral sin(x+x^2)/(x+x^4) dx? WolframAlpha can't solve it and i'm too(

@angelmendez-rivera351

5 жыл бұрын

our or This integral is very non-elementary, so there is nothing you can do to find a solution. It contains the already non-elementary integration of sin(x)/x, but with a function of the argument inside. It is totally insufferable.

If the red integral is = to the black integral , and both denominators are the same , dose that mean that both numerators are = ? If so tan(x)^root 2 =1 so the denominator of the red integral = 2 . How come the step with 2i equation is needed?

Impressive !

@ThePhenomBot

5 жыл бұрын

Moon Light pubg guy

Yeah...I like it..

What was the reason for him multiplying the I by 2? I understood everything after that, it's just wanted to know the rationale of multiplying the I by 2

@doctorb9264

3 жыл бұрын

adding 2 copies of the same integral.

my skin is peeling, tearing and reaping. my brain is melting, and my hair is falling

When do you use this technique?

When I look at the intro and it says Putnam : nope straight to the solution :P

There are three main properties in definite integral so they just gave them the names 1)king property 2) queen property 3) jack property According to my opinion

すごごごごごーーーー！！

Hi! you solve the problem but it ........so

This problem literally came in our unit test...

Hello guys...... I'm not champion in mathematics but I have doubt...on area under the curves..... See if I have an integral of x^3 dx from 1 to -1 ...so it covers the area under the X-axis so we can write it as 2*ingration of x^3dx .....because the area between 0to1 is same as the area between -1to0.....see the graph of x^3 and area should be positive... I gaused.. So the answer should be 1/2...but my professor told me that it was 0...and now I'm getting 😕 on that area..... So can somebody tell me why that is so ? 🙏🤒

@jaymenchang4243

5 жыл бұрын

You are correct saying that the area is the same in terms of regular terms (absolute value of the area magnitude wise) however when integrating we treat areas under the xaxis as negative, so the area from 0-1 is the negative of -1 to 0

@UjwalAroor

5 жыл бұрын

Actually that depends on the question.If your prof straight up just gave you a definite integral to solve then he is right.However if he specifically asked for the area under the curve then you are right. Usually area is positive so yeah.

@BigDBrian

5 жыл бұрын

Whenever the function is below 0 you can think of the area as being "signed" with a negative sign (-). Meaning that when you add it up with other areas, you actually subtract it when you take the integral.

@jaymenchang4243

5 жыл бұрын

Ujwal 9000 the problem with that intepretation is that from -1 to 0 the area is not "under the curve in fact its under the xaxis towards the curve, so the only way it would be "under the curve" is if the function was shifted vertically, or if you were asked to find the area between y= -1, x = 1 and the curve THEN u could interpret it as just the area under the curve, however the integral will give you the correct answer as f(x)-g(x) where g(x) is negative will yield a positive value

@quantumcity6679

5 жыл бұрын

@@jaymenchang4243 satisfying answer.... Thanks 👍😇

Every piece on chess board could have such a property.

Bprp is here to like everyone's comment ☺️☺️☺️☺️☺️😊😊

@kartiksharma7166

5 жыл бұрын

Now please solve this plsplspspplspspspplplsplspls x+x^2+x^4+x^8+x^16+ x^32+..... given |x|

This ques was less than 30sec for me by same method

When you use blue pen even though your channel's name is 'black pen red pen' haha.