Cho \(\int\limits_{0}^{\frac{\pi }{2}}{f(x)\text{d}x}=3\). Tính \(I=\int\limits_{0}^{\frac{\pi }{2}}{\left[ 2f(x)+\sin x \right]\text{d}x}\)

* Hướng dẫn giải

\(I = \int\limits_0^{\frac{\pi }{2}} {\left[ {2f(x) + \sin x} \right]{\rm{d}}x} = 2\int\limits_0^{\frac{\pi }{2}} {f(x){\rm{d}}x} + \int\limits_0^{\frac{\pi }{2}} {\sin x{\rm{d}}x} = 6 - \left. {\cos x} \right|_0^{\frac{\pi }{2}} = 6 + 1 = 7\)