Nếu π 2 ∫ 0 f ( x ) d x = − 5 thì π 2 ∫ 0 [ f ( x ) + sin x ] d x bằng

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Nếu \(\int\limits_0^{\frac{\pi }{2}} {f\left( x \right){\rm{d}}x} = - 5\) thì \(\int\limits_0^{\frac{\pi }{2}} {\left[ {f\left( x \right) + \sin x} \right]{\rm{d}}x} \) bằng

\( - 4\).

\( - 7\).

\( - 6\).

\( - 3\).

Giải thích

Ta có \(\int\limits_0^{\frac{\pi }{2}} {\left[ {f\left( x \right) + \sin x} \right]{\rm{d}}x} = \int\limits_0^{\frac{\pi }{2}} {f\left( x \right){\rm{d}}x} + \int\limits_0^{\frac{\pi }{2}} {\sin x{\rm{d}}x} = - 5 - \left. {\cos x} \right|_0^{\frac{\pi }{2}} = - 5 - \cos \frac{\pi }{2} + \cos 0 = - 4\).

Chọn A.