Cho \(I = \int\limits_0^{{\...

B

- Hướng dẫn giải

\(\begin{array}{l}{I_1} = \int\limits_0^{{\textstyle{\pi \over 3}}} {\left( {\sin 3x + {{\cos }^2}x} \right)dx} \\= \int\limits_0^{\frac{\pi }{3}} {\left( {\sin 3x + \frac{{1 + \cos 2x}}{2}} \right)dx} \\= \left. {\left( { - \frac{1}{3}\cos 3x + \frac{1}{2}x + \frac{1}{4}\sin 2x} \right)} \right|_0^{\frac{\pi }{3}}\\ \Rightarrow a = - \frac{1}{3},b = \frac{1}{2},c = \frac{1}{4} \\\Rightarrow 3a + 2c + 4c = 1\end{array}\)