Cho ∫f(x)dx=5. Khi đó ∫ [f(x)+2sinx]dx bằng:

Question

Cho \(\int _{0}^{\frac{\pi }{2} }f\left(x\right){\rm d}x=5 \).

Khi đó  \(\int _{0}^{\frac{\pi }{2} }\left[f\left(x\right)+2\sin x\right]{\rm d}x\)  bằng:

\( A. 5+\pi . \)

\(B. 5+\frac{\pi }{2} . \)

\(C. 7. \)

\(D. 3.\)

Answer 1

Chọn C.

Ta có: \(I=\int _{0}^{\frac{\pi }{2} }\left[f\left(x\right)+2\sin x\right]{\rm d}x \)

\(=\int _{0}^{\frac{\pi }{2} }f\left(x\right){\rm d}x+2\int _{0}^{\frac{\pi }{2} }\sin x{\rm d}x=5-  \left. 2\cos x\right|_{0}^{\frac{\pi }{2} }\)

\(=5-2\left(\cos \frac{\pi }{2} -\cos 0\right)=5+2=7\)