Cho \(\int^{\dfrac{\pi}{2}}_0f\left(x\right)\text{d}x=5.\) Tích phân \(\int^{\dfrac{\pi}{2}}_0\left(f\left(x\right)+2\sin x\right)\text{d}x\) bằng
\(7\).\(3\).\(5+\pi\).\(5+\dfrac{\pi}{2}\).Hướng dẫn giải:Ta có \(\int^{\dfrac{\pi}{2}}_0\left(f\left(x\right)+2\sin x\right)\text{d}x=\int^{\dfrac{\pi}{2}}_0f\left(x\right)\text{d}x+2\int^{\dfrac{\pi}{2}}_0\sin x\text{d}x=5-2\cos x|^{\dfrac{\pi}{2}}_0=5+2=7.\)