Question

Вычислить интеграл наверху (2p/3) снизу (0) 2sin (p/3+x)dx

Answer 1

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Answer 2

$\int\limits^{\frac{2\pi }{3}}_0\, 2sin(\frac{\pi}{3}+x)dx=-2\cdot cos(\frac{\pi}{3}+x)\Big |_0^{\frac{2\pi }{3}}=\\\\=-2\cdot (cos\pi -cos\frac{\pi}{3})=-2\cdot (-1-\frac{1}{2})=2\cdot  \frac{3}{2}=3\\\\\\\star \; \; \int sin(kx+b)\, dx=-\frac{1}{k}cos(kx+b)+C\; \; \star$