\(\left\{{}\begin{matrix}u=x\\dv=sin2xdx\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}du=dx\\v=-\dfrac{1}{2}cos2x\end{matrix}\right.\)
\(\Rightarrow I=-\dfrac{1}{2}x.cos2x|^{\dfrac{\pi}{3}}_0+\dfrac{1}{2}\int\limits^{\dfrac{\pi}{3}}_0cos2xdx=\dfrac{\pi}{12}+\dfrac{1}{4}sin2x|^{\dfrac{\pi}{3}}_0=\dfrac{\pi}{12}+\dfrac{\sqrt{3}}{8}\)
\(\Rightarrow\left\{{}\begin{matrix}a=12\\b=8\end{matrix}\right.\)
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