Question

П/2 интеграл 0 sinx/ корень cosx dx

Answer 1

$\int\limits^{\frac{\pi}{2}}_0 {\frac{sinx}{\sqrt{cosx}}} \, dx =\int _0^{\frac{\pi}{2}} \frac{-d(cosx)}{\sqrt{cosx}} =-2\sqrt{cosx}|_0^{\frac{\pi}{2}}=-2(\sqrt{0}-\sqrt1)=2\\\\\\d(cosx)=(cosx)'dx=-sinx\, dx\\\\\int \frac{dt}{\sqrt{t}} =2\sqrt{t}+C$