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Câu hỏi: Cho $\int\limits_{0}^{\dfrac{\pi }{2}}{f\left( x \right)}\text{d}x=4$. Khi đó $\int\limits_{0}^{\dfrac{\pi }{2}}{\left[ 2f\left( x \right)+\sin x \right]}\text{d}x$ bằng
A. $8+\dfrac{\pi }{2}.$
B. $4+\pi .$
C. $9.$
D. $7.$
A. $8+\dfrac{\pi }{2}.$
B. $4+\pi .$
C. $9.$
D. $7.$
Ta có $\int\limits_{0}^{\dfrac{\pi }{2}}{\left[ 2f\left( x \right)+\sin x \right]}\text{d}x=2\int\limits_{0}^{\dfrac{\pi }{2}}{f\left( x \right)}\text{d}x+\int\limits_{0}^{\dfrac{\pi }{2}}{\sin x}\text{d}x=2\cdot 4+1=9.$
Đáp án C.
