• # question_answer Let $f\,(x)=\left| \begin{matrix} 2{{\cos }^{2}}x & \sin \,(2x) & -\sin x \\ \sin 2x & 2{{\sin }^{2}}x & \cos x \\ \sin x & -\cos x & 0 \\ \end{matrix} \right|$ then $\int\limits_{0}^{\pi /2}{[f\,(x)+f'\,(x)]\,\,dx=}$ A)  $\pi$ B) $\pi /2$ C) $2\pi$ D) zero

Use ${{c}_{2}}\to {{c}_{2}}+2\cos x\,\,{{c}_{3}}$$\Rightarrow$$f\,(x)=2$$\Rightarrow$$f'\,(x)=0$