Cho giá trị của tích phân \...

A

- Hướng dẫn giải

\({I_1} = \int\limits_{ - \frac{\pi }{2}}^{\frac{\pi }{3}} {\left( {\sin 2x + \cos x} \right)dx} = \left. {\left( { - \frac{1}{2}\cos 2x + \sin x} \right)} \right|_{ - \frac{\pi }{2}}^{\frac{\pi }{3}} = \frac{3}{4} + \frac{{\sqrt 3 }}{2} \Rightarrow a = \frac{3}{4} + \frac{{\sqrt 3 }}{2}\)

\({I_2} = \int\limits_{ - \frac{\pi }{3}}^{\frac{\pi }{3}} {\left( {\cos 2x + \sin x} \right)dx} = \left. {\left( {\frac{1}{2}\sin 2x - \cos x} \right)} \right|_{ - \frac{\pi }{3}}^{\frac{\pi }{3}} = \frac{{\sqrt 3 }}{2} \Rightarrow b = \frac{{\sqrt 3 }}{2}\)

\( \Rightarrow P = a + b = \frac{3}{4} + \sqrt 3 \)