Question

Help what is

[\int_{0}^{\pi} \sin(x) \cos(x) ,dx]

Answer 1

oh thats

Answer 2

JRUEREUERE828827262629020332423234=000=0+++//./...\.\.

Answer 3

Well as we can see it's letter's, numbers and symbols

Answer 4

letters'

Answer 5

\[[\int\limits_{0}^{\pi} \sin(x) \cos(x) ,dx]\]

this is what that is and I have ni idea how to solve that

Answer 6

https://www.gauthmath.com/search-question?questionID=1780225567161349&action=image_search&position=search_edge_card

Answer 7

this is app to solve math

Answer 8

\[let~I=\int\limits_{0}^{\pi} \sin x \cos x~dx\]
\[=\frac{ 1 }{ 2 }\int\limits_{0}^{\pi}2\sin x \cos x ~dx\]
\[=\frac{ 1 }{ 2 }\int\limits_{0}^{\pi}\sin 2x dx\]
put 2x =t
2dx=dt
when x=0,t=0
when x=pi
t=2 pi
\[I=\frac{ 1 }{ 2 }\int\limits_{0}^{2\pi}\sin t~\frac{ dt }{ 2 }=\frac{ 1 }{ 4}\int\limits_{0}^{2 \pi} \sin t~dt\]
\[\sin (2\pi-t)=\sin t \]
\[I=2\times \frac{ 1 }{ 4}\int\limits_{0}^{\pi}\sin t dt=\frac{ 1 }{ 2 }\int\limits_{0}^{\pi}\sin t~dt\]
\[\sin (\pi-t)=\sin t\]
\[I=2\times \frac{ 1 }{2 }\int\limits_{0}^{\frac{ \pi }{2 }}\sin t~dt=[-\cos t] ~0~\to~\frac{ \pi }{ 2}\]
\[=-(\cos \frac{ \pi }{ 2 }-\cos 0)=-(0-1)=1\]