Question

Integrate : sin pi/3 cos pi/3 dx

Answer 1

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

Answer 2

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