Question

If $\frac{dy}{dx}=\cos \left(2x\right)$, then $y=$

• A. $\frac{\sin \left(2x\right)}{2}+c$
• B. $2\sin \left(2x\right)+c$
• C. $\frac{\sin \left(x\right)}{2}+c$
• D. None of these

Answer 1

The correct option is A $\frac{\sin \left(2x\right)}{2}+c$

Using substitution method.
$u=2x$
$du=2dx$
$\frac{du}{2}=dx$
Plug in.
$dy=\frac{1}{2}cos\left(u\right)du$
Integrate.
$y=\frac{sin\left(2x\right)}{2}+c$