Biết rằng \(I=\int\limits_{0}^{1}{x\cos 2xdx}=\frac{1}{4}\left( a\sin 2+b\cos 2+c \right)\) với \(a,b,c\in Z\). Mệnh đề nào sau đây là đúng?

\(I = \int\limits_0^1 {x\cos 2xdx} \) đặt \(\left\{ \begin{array}{l}
u = x\\
dv = \cos 2xdx
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
du = dx\\
v = \frac{{\sin 2x}}{2}
\end{array} \right. \Rightarrow I = \left. {x.\frac{{\sin 2x}}{2}} \right|_0^1 – \frac{1}{2}\int\limits_0^1 {\sin 2xdx} \)

\(\begin{array}{l}
I = \frac{{\sin 2}}{2} + \frac{1}{2}.\left. {\frac{{\cos 2x}}{2}} \right|_0^1 = \frac{{\sin 2}}{2} + \frac{1}{4}\left( {\cos 2 – 1} \right) = \frac{1}{4}\left( {2\sin 2 + \cos 2 – 1} \right) = \frac{1}{4}\left( {a\sin 2 + b\cos 2 + c} \right)\\
\Rightarrow \left\{ \begin{array}{l}
a = 2\\
b = 1\\
c = – 1
\end{array} \right. \Rightarrow a – b + c = 0
\end{array}\)

Chọn A.