Gold 2

Ellipse

Gold ID

2

Link

https://sigir21.wmflabs.org/wiki/Ellipse#math.52.404

Formula

$E(e)\,=\,\int _{0}^{\pi /2}{\sqrt {1-e^{2}\sin ^{2}\theta }}\ d\theta$

TeX Source

E(e) \,=\, \int_0^{\pi/2}\sqrt {1 - e^2 \sin^2\theta}\ d\theta

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\compellintEk@{\expe} = \int_0^{\cpi / 2} \sqrt{1 - \expe^2 \sin^2 \theta} \diff{\theta}

Expected (Gold Entry)

\compellintEk@{e} = \int_0^{\cpi / 2} \sqrt{1 - e^2 \sin^2 \theta} \diff{\theta}

Mathematica

Translation

EllipticE[(E)^2] == Integrate[Sqrt[1 - Exp[2]*(Sin[\[Theta]])^(2)], {\[Theta], 0, Pi/2}, GenerateConditions->None]

Expected (Gold Entry)

EllipticE[(e)^2] == Integrate[Sqrt[1 - (e)^(2)*(Sin[\[Theta]])^(2)], {\[Theta], 0, Pi/2}]

Maple

Translation

EllipticE(exp(1)) = int(sqrt(1 - exp(2)*(sin(theta))^(2)), theta = 0..Pi/2)

Expected (Gold Entry)

EllipticE(e) = int(sqrt(1 - (e)^(2)*(sin(theta))^(2)), theta = 0..Pi/2)