Integrate : sin pi/3 cos pi/3 dx

Question

michele_laino · Answer

hint: we have the subsequent steps:
$$\Large \begin{gathered}
  \int {\sin \left( {\frac{\pi }{3}} \right)\cos \left( {\frac{\pi }{3}} \right)\;dx}  = \int {\frac{1}{2} \cdot \sin \left( {\frac{{2\pi }}{3}} \right)\;dx}  =  \hfill \
   \hfill \
   = \frac{1}{2} \cdot \sin \left( {\frac{{2\pi }}{3}} \right)\int {dx}  = ...? \hfill \ 
\end{gathered} $$

anonymous · Answer

$$\int\limits \sin \frac{ \pi }{ 3 }  \cos \frac{ \pi }{ 3 }dx = \frac{ 1 }{ 2 } \int\limits 2 \sin \frac{ \pi }{ 3 }  \cos \frac{ \pi }{ 3 }dx\ =\frac{ 1 }{ 2 } \int\limits \sin\frac{ 2\pi }{ 3}dx\= \frac{ 1 }{ 2 }\frac{ -\cos \frac{ 2\pi }{ 3 } }{ \frac{ 2 }{ 3 } } + K\ = \ \frac{- 3 }{ 4 }\cos \frac{ 2\pi }{ 3}+K  (Ans)$$