Were there any options? I am asking because as Anish said that the value of the integral has no clear form. Maybe they intended to ask something different??

There is no exact formula but use the famous Indian mathematician Ramanujan came up with this better approximation:search Ramanujan circumference of ellipse formula

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TopNewestLet the ellipse be : \(\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2} = 1\)

Parametric coordinates : \(\displaystyle (x,y) = (a\cos\theta,b\sin\theta)\)

\[ds^2 = dx^2+dy^2\]

\[ds^2 = \left((\frac{dx}{d\theta})^2 + (\frac{dy}{d\theta})^2\right)d\theta^2\]

\[ds^2 = (a^2\sin^2\theta+ b^2\cos^2\theta)d\theta^2\]

\[ds = \sqrt{(a^2\sin^2\theta+ b^2\cos^2\theta)}d\theta\]

Integrate it from \(\displaystyle 0\) to \(\displaystyle 2\pi\), and you will get the result.

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Good luck integrating that monster.! (it hasn't been solved yet)

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i am surprised This question came in VIT couldnt solve it maths was at a good level indeed when is urs or have u already given it

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Were there any options? I am asking because as Anish said that the value of the integral has no clear form. Maybe they intended to ask something different??

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\(\pi(2^{1/2}),2\pi(2^{1/2}),\pi(2+2^{1/2})\) and one other i dont remember them clearly

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There is no exact formula but use the famous Indian mathematician Ramanujan came up with this better approximation:search Ramanujan circumference of ellipse formula

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