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in Definite Integrals by (20 points)
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\( \int_{\pi / 6}^{\pi / 3} \sin (3 x) d x= \)

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Let \(I = \int\limits_{\frac{\pi}6}^{\frac{\pi}3} sin(3x)dx\) 

\(= \left[\frac{-cos(3x)}{3}\right]^{\frac{\pi}3}_{\frac{\pi}{6}}\)

\(= \frac{-1}3\left(cos \pi - cos \frac{\pi}{2}\right)\)

\(= \frac{-1}{3}(-1-0)\)

\(= \frac13\)

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