Question

Can someone help me find the integration by substitution of a problem, I'm having a bit of problems with the trig in there. Thanks :)

Answer 1

\[\int\limits_{0}^{\frac{ \pi }{ 4 }}\sin (2x)dx=\]

Answer 2

so far i have
u=2x
du=2dx
\[\frac{ 1 }{ 2 }\int\limits_{0}^{\frac{ \pi}{ 4 }}\sin (u)2du\]
\[-\frac{ 1 }{ 2 }\cos (u)+c\]
\[-\frac{ 1 }{ 2 }\cos (2x)\]
F(b)-F(a)
\[-\frac{ 1 }{ 2 }\cos(2(\frac{ \pi }{ 4 }))-[-\frac{ 1 }{ 2 }\cos (2(0))] \]

Answer 3

I'm having a bit of problem with the next part