\(\dfrac{{\sin 2x\sin x}}{2} + {\cos ^3}x\)\( = {\sin ^2}x\cos x + {\cos ^3}x\) \( = \cos x\left( {{{\sin }^2}x + {{\cos }^2}x} \right) = \cos x\)
\( \Rightarrow \int\limits_{ - \dfrac{\pi }{2}}^{\dfrac{\pi }{2}} {\left( {\dfrac{{\sin 2x\sin x}}{2} + {{\cos }^3}x} \right)dx} \) \( = \int\limits_{ - \dfrac{\pi }{2}}^{\dfrac{\pi }{2}} {\cos xdx} = \left. {\sin x} \right|_{ - \dfrac{\pi }{2}}^{\dfrac{\pi }{2}}\) \( = 1 - \left( { - 1} \right) = 2\).
Chọn A.
