Câu 41:

Cho hàm số $f\left( x \right)=\left\{ \begin{align} & 2x-4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{khi}\,x\ge 4 \\ & \frac{1}{4}{{x}^{3}}-{{x}^{2}}+x\,\,\,\text{khi}\,x<4 \\\end{align} \right.$. Tích phân $\int\limits_{0}^{\frac{\pi }{2}}{f\left( 2{{\sin }^{2}}x+3 \right)\sin 2x\text{d}x}$ bằng

Câu 41:

Cho hàm số f\left( x \right)=\left\{ \begin{align} &amp; 2x-4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{khi}\,x\ge 4 \\ &amp; \frac{1}{4}{{x}^{3}}-{{x}^{2}}+x\,\,\,\text{khi}\,x&lt;4 \\\end{align} \right.. Tích phân $\int\limits_{0}^{\frac{\pi }{2}}{f\left( 2{{\sin }^{2}}x+3 \right)\sin 2x\text{d}x}$ bằng