Question

Im trying to intergrate 5sin3x where x is between 0 and (pi)/5 some people say i need to do intergration by parts, Ive gone done to -3(5cos3(Pi/5))+5sin3(pi/5) is this correct?

Answer 1

\[I=\int\limits_{0}^{\frac{ \pi }{5 }}5\sin 3x dx=\frac{ -5 }{3 }\cos 3x ,x ,0\rightarrow \frac{ \pi }{ 5 }\]
\[=\frac{ -5 }{ 3 }\left[ \cos \frac{ 3\pi }{ 5 }-\cos 0 \right]=\frac{ -5 }{ 3 }\left[ \cos 108-1 \right]\]
\[=\frac{ 5 }{3 }\left[ 1-\cos \left( 180-72 \right) \right]=\frac{ 5 }{3 }\left[ 1+\cos 72 \right]\]
now you can calculate.

Answer 2

Thanks alot

Answer 3

yw