I love your solution development. It's streight forward and you don't hold up with obvious exploration of trivial matter. Your presenting speed is all right and your speech clear even for non native listeners . This is a great advantage compared to several other math channels.
I loved whenever you say sinh and cosh. Try to add TAMIL in audio track. For Direchlet's integral you left Lobachevsky's rule. It's the very easy method to solve it
Yes, the integral e^ix /x should equal I Pi. But since the desired integral of sin x / x is the imaginary part of that solution, the imaginary part is simply pi, as written on the next line.
Hello sir, feel free to solve this integral whenever you want, but I’d really like seeing it in one of your videos! The integral is from 0 to inf of (e^-x)/((Gamma(3/2 + x))(Gamma(1/2-x))), this integral involves the exponential integral! Ei(x) if I’m right, which you barely show in your videos! I’d be glad to see your solution :))
The man the myth the legend has returned to post once again! Just checking, you use Samsung Notes app for these videos? I'm thinking of starting a maths channel too using my Note, focused on much simpler algebra problems. What are some tips and tricks to making these videos with smooth transitions etc.? I've practiced writing on the screen and I must say your handwriting is almost flawless, do you use a screen protector at all? I can't get mine to look neat no matter how slowly I write.
@@zunaidparker yeah I use a screen protector. I used one back when I used to record on my phone too. I think it's down to practice, I've been using a note phone since 2018 when I bought a note 4 and I've always loved the s pen feature so it just grew on me over the years.
@@zunaidparker as far as the transitions are concerned, I just record a clip of 4 or 5 minutes and then another until the video is complete and stitch it all together using capcut
Since these are definite integrals (with limits), once you do the substitution it doesn't matter what they once were. If they were indefinite integrals you'd be right, but that also doesn't matter much as indefinite integrals can't combine like that.
@@kavimahajan8412they are the same as sin and cos but rotated by π/2 in the complex plane. So on the imaginary axis sinh and cosh are oscillatory and on the real axis sin and cos are oscillatory. Alternatively, sinh and cosh are defined such that cosh²x-sinh²x≡1. Representing the x and y parts of a hyperbola, like cos and sin represent the x and y parts of a circle.
they’re like the ‘imaginary version’ of sin and cos: cosh(x) = cos(ix) sinh(x) = -i*sin(ix) and because of this they obey a lot of formulas/identities very similar to trig identities
What both these guys above said, additionially just like how (sin(t),cos(t)) describes a point on the circle x^2+y^2=1, (cosh(t),sinh(t)) describes a point on the hyperbola x^2-y^2=1. Planet orbits are usually circular, but if a planet exceeds its escape velocity, or a comet flies by a star, its "orbit" will be hyperbolic.
"The Hindu religion is the only one of the world's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang." “Most cultures imagine the world to be a few hundred human generations old. Hardly anyone guessed that the cosmos might be far older but the ancient Hindus did,” "It is the only religion in which the time scales correspond, to those of modern scientific cosmology" ~ CARL SAGAN (famous astronomer, cosmologist)
I love your solution development. It's streight forward and you don't hold up with obvious exploration of trivial matter. Your presenting speed is all right and your speech clear even for non native listeners . This is a great advantage compared to several other math channels.
I concur
@@wowbagger7168 thank you
I loved whenever you say sinh and cosh. Try to add TAMIL in audio track. For Direchlet's integral you left Lobachevsky's rule. It's the very easy method to solve it
amazing as always! one thing: 14:06 there should be an ‚i‘ in front of the Pi right?
That's correct
Yes, the integral e^ix /x should equal I Pi. But since the desired integral of sin x / x is the imaginary part of that solution, the imaginary part is simply pi, as written on the next line.
Thank you for your effort.
this was awesome
I'd say it was...
Worth the hyp😎
Hello sir, feel free to solve this integral whenever you want, but I’d really like seeing it in one of your videos! The integral is from 0 to inf of (e^-x)/((Gamma(3/2 + x))(Gamma(1/2-x))), this integral involves the exponential integral! Ei(x) if I’m right, which you barely show in your videos! I’d be glad to see your solution :))
Excellent
Very goooooood
The man the myth the legend has returned to post once again!
Just checking, you use Samsung Notes app for these videos? I'm thinking of starting a maths channel too using my Note, focused on much simpler algebra problems. What are some tips and tricks to making these videos with smooth transitions etc.? I've practiced writing on the screen and I must say your handwriting is almost flawless, do you use a screen protector at all? I can't get mine to look neat no matter how slowly I write.
@@zunaidparker yeah I use a screen protector. I used one back when I used to record on my phone too. I think it's down to practice, I've been using a note phone since 2018 when I bought a note 4 and I've always loved the s pen feature so it just grew on me over the years.
@@zunaidparker as far as the transitions are concerned, I just record a clip of 4 or 5 minutes and then another until the video is complete and stitch it all together using capcut
Third from last equation should have pi * i on rhs
Hey kammal!
I have a quick question. Where do you get all these nice problems? Thx! Great video!
00:43 I tried doing this is physics last year lmao
Legendary stuff😂
Good work. What about a hyperbolic trig integral?
On it
why are you allowed to combine those integrals at 4:04, to me that feels wrong, because the one u = e^x and the other u = e^-x ?
Since these are definite integrals (with limits), once you do the substitution it doesn't matter what they once were. If they were indefinite integrals you'd be right, but that also doesn't matter much as indefinite integrals can't combine like that.
@Sam27182 ah ok
Someone explain hyperbolic trig to me
Like I know how to express them with the exponential but how is that related to sin or cos
@@kavimahajan8412they are the same as sin and cos but rotated by π/2 in the complex plane. So on the imaginary axis sinh and cosh are oscillatory and on the real axis sin and cos are oscillatory.
Alternatively, sinh and cosh are defined such that cosh²x-sinh²x≡1. Representing the x and y parts of a hyperbola, like cos and sin represent the x and y parts of a circle.
they’re like the ‘imaginary version’ of sin and cos:
cosh(x) = cos(ix)
sinh(x) = -i*sin(ix)
and because of this they obey a lot of formulas/identities very similar to trig identities
What both these guys above said, additionially just like how (sin(t),cos(t)) describes a point on the circle x^2+y^2=1, (cosh(t),sinh(t)) describes a point on the hyperbola x^2-y^2=1. Planet orbits are usually circular, but if a planet exceeds its escape velocity, or a comet flies by a star, its "orbit" will be hyperbolic.
"The Hindu religion is the only one of
the world's great faiths dedicated to
the idea that the Cosmos itself
undergoes an immense, indeed an
infinite, number of deaths and
rebirths. It is the only religion in which
the time scales correspond to those of
modern scientific cosmology. Its
cycles run from our ordinary day and
night to a day and night of Brahma,
8.64 billion years long. Longer than
the age of the Earth or the Sun and
about half the time since the Big
Bang."
“Most cultures imagine the world to be a few hundred human generations old. Hardly anyone guessed that the cosmos might be far older but the ancient Hindus did,”
"It is the only religion in which the time scales correspond, to those of modern scientific cosmology"
~ CARL SAGAN (famous astronomer, cosmologist)
integral hype