Matematické Fórum

stuart clark · 14. 05. 2014 05:54

$(1)$ How Can we prove $\displaystyle \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\sqrt{\frac{\cos 2 \phi}{2\cos^2 \phi}}\right)d\phi = \frac{\pi^2}{24}$

$(2)$ How Can we prove that $\displaystyle \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi = 0$

Matematické Fórum

#1 14. 05. 2014 05:54

2 definite Integrals

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