#integralchallenge — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #integralchallenge, aggregated by home.social.
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Take a look at this interesting integral. #MathsChallenge [Hint: use the properties of the Jacobi theta function of the third type \(\vartheta_3(z,q)\)]
\[\boxed{\displaystyle\int_0^{\frac{\pi}{4}}\dfrac{1+2\displaystyle\sum_{n\geq1}e^{-n^2\pi x}}{1+2\displaystyle\sum_{n\geq1}e^{-n^2\pi/x}}\ \mathrm{d}x=\sqrt\pi}\]
#MathChallenge #IntegralChallenge #InterestingIntegral #WeirdIntegral #Integral #Integrals #DefiniteIntegral
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Integral challenge!
\[\displaystyle\int_0^\infty\ln\left(1+\dfrac{\cosh\alpha}{\cosh x}\right)\ dx=\dfrac{\pi^2}{8}-\dfrac{\arccos^2(\cosh\alpha)}{2}\]
#Integral #Integrals #IntegralChallenge #HyperbolicFunction #HyperbolicCosine #Logarithm #DefiniteIntegral