Use properties of definite integrals, replace θ by (π/2 - θ) and add both I. Pretty straight forward and easier haha.

@maths_505

9 күн бұрын

Oh yeah 😂 but this is more fun

@user-lu6yg3vk9z

8 күн бұрын

@@maths_505why didn’t u use kings property?

@famillemagnan1313

8 күн бұрын

Much easier indeed!

@manjugangwar7245

7 күн бұрын

I used the same

Love when he writes π as a и with - on top of it

@vladthemagnificent9052

8 күн бұрын

ln, sin, and tan also looks like lu siu and tau

Replacing theta with x, the curve is symmetric with respect to the segment from (0,2) to (pi/2,0), so the area of that triangle is pi/2.

i encountered this integral in school: integral from 0 to 1 of xe^x, i obviously solved it using integration by parts and it resulted in 1 but i tried to generalize it using a parameter alpha in the exponent of x so i got the integral of x^alpha*e^x but i'm not smart enough to solve it and i would love to see it in one of the next videos. also i love watching your videos, especially at night since they're so relaxing and they help me falling asleep. great work! keep it up

Ohh man just replace θ by (π/2 - θ) And then add both. You'll get, 2 I = ∫ { ln(tan²θ) / ln(tanθ) }dθ = ∫ 2 dθ = π I = π/2

This is gorgeous, thank you very much.

Some people are somehow not happy with you not using that easy 2 liner solution. But (at least to me), this one was way more fun. I think sometimes, the way matters more than the result. And Ik it's better to have a simple solution, but still sometimes the complex one is the one which actually seems interesting and more fun. So thanks!

@maths_505

9 күн бұрын

Thanks for getting it homie

@SussySusan-lf6fk

7 күн бұрын

Yep 😊

A wild integral representation of pie.

Basically this is saying the magnitude of sin2theta relative to tantheta along the first quadrant changes by a rate of pi/2 (up to a constant).

The integral reduces to int(1)dx from 0 to pi/2 using King, Log, and Trig properties without substitution.

Here's the solution in 3-4 line -- I= ∫ [ (stuff) -1+1]d∅ now take lcm With -1 U will find inside logarithms upstairs ln(sin2∅) Downstairs ln(tab∅) You have listen about The KINGS rule apply to the above integral and you will find the integral collapse 0 , ∫d∅ from π/2to 0 = π/2 ans

Greetings Kamal, i also forget how to talk from time to time 😂😂

At the point where you expand by e^x/2 (9:08), the integrand readily becomes sech(x/2) when multiplied by 2. 1/2Integrate[Sech[x/2], x,-infy,infy] Nevertheless, the z-substitution afterward was nifty.

It's all making sense now, the Black speech of Mordor, sounded very scary when I was a child, cause it was all maths.😁 I even got some hints for this to be true at school, when writting a test, and I looked to my neighbours test for a second, the teacher gave me a nasty look, and said "I see yooouuu."😅

Another dope integral representation of π

Using the change of variable u=pi/2 - thêta, and addint it to the initial integral leads to the results much faster. (A bit frustrated for you not using it)

Nice!

@maths_505

9 күн бұрын

Thanks mate

Hi, "ok, cool" : 1:11 , 1:56 , 2:29 , 3:46 , "Terribly sorry about that" : 4:55 , 6:31 .

i didnt understand the part where u say as x is an odd function but the others are even functions ,due to even f(x) the integral converges to zero from negative to positive infinity

Mi sembra troppo semplice 2I=Int(2)dx(0...π/2)=π..I=π/2

Is there any textbook for these kimd of question

Which country are you from? Your are videos are so good

@maths_505

9 күн бұрын

I'm from Pakistan

No beta function??, are you okay??

@trelosyiaellinika

8 күн бұрын

😂