Question

Интеграл от p/4 до p/2 sin2xdx

Answer 1

$\large \int_{\pi\over4}^{\pi\over2}\sin{(2x)}\mathrm{dx}={1\over2}\int_{\pi\over4}^{\pi\over2}\sin{(2x)}\mathrm{d(2x)}=-{\cos{(2x)}\over2}|_{\pi\over4}^{\pi\over2}=-{\cos{\pi}\over2}+{\cos{\pi\over2}\over2}={1\over2}(\cos{\pi\over2}-\cos{\pi})={1\over2}$