6. Вычислите интеграл ∫(от π/4 до π/2) 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} = 6 * (sin(\frac{2(\pi/2)}{3}) - sin(\frac{2(\pi/4)}{3})) = 6 * (sin(\frac{\pi}{3}) - sin(\frac{\pi}{6})) = 6 * (\frac{\sqrt{3}}{2} - \frac{1}{2}) = 3(\sqrt{3} - 1)