Cho hàm số f(x) = căn bậc hai của x +2 khi x lớn hơn hoặc bằng 0

Câu hỏi :

Cho hàm số $f\left(x\right)=\left\{\begin{array}{l}\sqrt{x}+2\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}khi\hspace{0.17em}}x\ge 0\\ 3x^2-x+2\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}khi\hspace{0.17em}}x<0\end{array}\right.$. Tích phân $\underset{0}{\overset{\frac{\pi }{3}}{\int }}f\left(3-4\cos x\right)\sin x\text{d}x$ bằng