Cho pi /2 f(x) dx = 5 . Tính f(x) + 2 sin x ) dx = 5

6/22

Cho \(\int\limits_0^{\frac{\pi }{2}} {f\left( x \right){\rm{d}}x} = 5\). Tính \(I = \int\limits_0^{\frac{\pi }{2}} {\left[ {f\left( x \right) + 2\sin x} \right]{\rm{d}}x} = 5\).

\(I = 7\).

\(I = 5 + \frac{\pi }{2}\).

\(I = 3\).

\(I = 5 + \pi \)

Giải thích

Chọn A

Ta có

\(I = \int\limits_0^{\frac{\pi }{2}} {\left[ {f\left( x \right)\, + 2\sin x} \right]\,{\rm{d}}x = \int\limits_0^{\frac{\pi }{2}} {f\left( x \right)\,{\rm{d}}x\,{\rm{ + 2}}\int\limits_0^{\frac{\pi }{2}} {\sin x} dx} } \)\( = \int\limits_0^{\frac{\pi }{2}} {f\left( x \right)} \,{\rm{d}}x\,\, - 2\cos x\left| \begin{array}{l}\frac{\pi }{2}\\0\end{array} \right. = 5 - 2\left( {0 - 1} \right) = 7\).