Cho hàm số y=f(x) = x^2 +3 khi x lớn hơn hoặc bằng 1 5-x khi x <1. Tính

* Hướng dẫn giải

Chọn B

$\begin{array}{l}I=2{\int }_0^{\frac{\pi }{2}}f\left(\sin x\right)\cos x\text{d}x+3{\int }_0^{1}f\left(3-2x\right)\text{d}x\\ \text{ =}2{\int }_0^{\frac{\pi }{2}}f\left(\sin x\right)\text{d}\left(\sin x\right)-\frac{3}{2}{\int }_0^{1}f\left(3-2x\right)\text{d}\left(3-2x\right)\\ \text{ =}2{\int }_0^{1}f\left(x\right)\text{d}x+\frac{3}{2}{\int }_1^{3}f\left(x\right)\text{d}x\\ =2{\int }_0^1\left(5-x\right)\text{d}x+\frac{3}{2}{\int }_1^3\left(x^2+3\right)\text{d}x\\ =9+22=31\end{array}$