6. Вычислите интеграл ∫(π/4) 4cos(2x/3)dx

\int_{\pi/4}^{\pi/2} 4cos(\frac{2x}{3})dx = [4 * \frac{3}{2}sin(\frac{2x}{3})]_{\pi/4}^{\pi/2} = [6sin(\frac{2x}{3})]_{\pi/4}^{\pi/2}
= 6sin(\frac{2(\pi/2)}{3}) - 6sin(\frac{2(\pi/4)}{3}) = 6sin(\frac{\pi}{3}) - 6sin(\frac{\pi}{6})
= 6 * \frac{\sqrt{3}}{2} - 6 * \frac{1}{2} = 3\sqrt{3} - 3