Question Number 213871 by 073 last updated on 19/Nov/24
Commented by Frix last updated on 19/Nov/24
$$\mathrm{Elliptic}\:\mathrm{Integral}: \\ $$$$\mathrm{4}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\sqrt{{a}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:{x}\:+{b}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:{x}}\:{dx}=\mathrm{4}{a}\mathrm{E}\:\left(\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\right) \\ $$