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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

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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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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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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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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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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