Integral of 1/(4-cos(x))^2 from 0 to pi

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Integral of (a-cos(x))^2, from 0 to pi,

Integral of 1/(4-cos(x))^2 from 0 to pi
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Комментарии
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I did this another way. Consider the ellipse with the equation in polar coordinates with the equation r=1/(4-cos(θ)). The area is equal to 1/2 times the integral. You can convert the equation into rectangular coordinates to find the radii and thus the area.

JoeMansley
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"I did this on my head" Flashbacks

joso
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Thank you sir... I'm head over heels in your teachnic of solving these integral

bipinmaurya
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You got that, man! I don't know, but this video looks so minimalist.

EduardoHerrera-frbd
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I can't even focus on the video because of that shirt you're wearing. Where can I get one of my own? I NEED IT!!!

alkankondo
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Now u using leibniz rule so this is definitely a super cool video 😀😀😀 yay

sergioh
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I found the antiderivative after 2 pages of calculation and then plugged in the limits and then arrived at the correct answer lol

Shishir
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And it doesn't matter of the cos is adding or substracting, because the original integral from 0 to Pi (the one with a) is still the same :)

hc_
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Why cant u just integrate it as a chain rule

pasq
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Feynam's trick! Yay! BTW, when can we not use Leibniz Rule? (bring d/da inside turning it into ∂/∂a) I have seen this trick used multiple times, but haven't learned multivariable calc yet.

temurson
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So the defined integral from 0 to pi of 1/(a-cosx)^3 dx = [pi(2a^2+1)]/[2(a^2-1)^(5/2)]

EduardoHerrera-frbd
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is there any website where i can download GaoKao test problems?

alfiangunawan
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can you show it by weierstrass substitution?

lightyagami
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at the end you got just a number for the solution, but if you take the derivative of a number its just zero, how can that be?

ofirmsh
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A good derivation. Show how to make new equations by differentiation. And maybe "+C" or not due to numerical limits. But it might still be applicable...

jarikosonen
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Do you think we could get better? Like the defined integral from 0 to pi or 1/(a-cosx)^n dx.

EduardoHerrera-frbd
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How I saw the start of this.

Me: gosh this is hard I like it to be simple.
"We are all adults know, so pause the video and try this yourself."

zeldasama
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Sir can you do it....???
Integration of {Sin(x)}^(1/2) dx.
I love your technique of math...

rishidas
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oh man got a crush on you you so great! hahaha

jaysonmatchado
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Can you intrgrate 1/(x+sqrt(1-x^2)) between 0 and 1 please. I am getting a very slightly different answer to my calculator and wolfram

Thedon-xygm