Cho \(\int\limits_0^{\frac{\pi }{2}} {f(x)\text{d}x = 5}\) . Tích phân \(\int\limits_0^{\frac{\pi }{2}} {\left[ {f(x) + 2\sin x} \right]} \text{d}x\) bằng
\(7\). \(3 \). \( 5 + \frac{\pi }{2} \). \( 5 + \pi \). Hướng dẫn giải: \(I = \int\limits_0^{\frac{\pi }{2}} {\left[ {f(x) + 2\sin x} \right]} \text{d}x = \int\limits_0^{\frac{\pi }{2}} {\left[ {f(x)} \right]} \text{d}x + \int\limits_0^{\frac{\pi }{2}} {\left[ {2\sin x} \right]} \text{d}x = 5 + 2 = 7\).