$\int_{0}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{4}}{[\cos (2t)\mathbf{i}+\sin (2t)\mathbf{j}+t\sin t\mathbf{k}]}\operatorname{dt}=$( ) A: $(\frac{1}{2},\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ B: $(1,\frac{1}{2},\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ C: $(\frac{1}{2},1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$ D: $(1,1,\frac{4-\text{ }\!\!\pi\!\!\text{ }}{4\sqrt{2}})$

Text 1

从原点向曲线$$y=1-\ln x$$作切线，则由切线、曲线和$$x$$轴围成图形的面积为()． A: $$\frac{1}{2}{{\text{e}}^{2}}+\text{e}$$ B: $$\frac{1}{2}{{\text{e}}^{2}}-\text{e}$$ C: $${{\text{e}}^{2}}+\text{e}$$ D: $${{\text{e}}^{2}}-\text{e}$$

Skim the text and answer the following questions. 1) What type of writing is the text?

函数$f(x)=x+\sin x$的( )。 A: 上凸区间为$(2n\text{ }\!\!\pi\!\!\text{ },(2n+1)\text{ }\!\!\pi\!\!\text{ })$,下凸区间为$((2n-1)\text{ }\!\!\pi\!\!\text{ },2n\text{ }\!\!\pi\!\!\text{ })$ B: 上凸区间为$((2n-1)\text{ }\!\!\pi\!\!\text{ },2n\text{ }\!\!\pi\!\!\text{ })$,下凸区间为$(2n\text{ }\!\!\pi\!\!\text{ },(2n+1)\text{ }\!\!\pi\!\!\text{ })$ C: 上凸区间为$(n\text{ }\!\!\pi\!\!\text{ },(n+1)\text{ }\!\!\pi\!\!\text{ })$,下凸区间为$((n-1)\text{ }\!\!\pi\!\!\text{ },n\text{ }\!\!\pi\!\!\text{ })$ D: 上凸区间为$((n-1)\text{ }\!\!\pi\!\!\text{ },n\text{ }\!\!\pi\!\!\text{ })$,下凸区间为$(n\text{ }\!\!\pi\!\!\text{ },(n+1)\text{ }\!\!\pi\!\!\text{ })$

已知齐次方程$(x-1){{y}^{''}}-x{{y}^{'}}+y=0$的通解为$Y={{C}_{1}}x+{{C}_{2}}{{e}^{x}}$，则方程$(x-1){{y}^{''}}-x{{y}^{'}}+y={{(x-1)}^{2}}$的通解是( ) A: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-({{x}^{2}}+1)$ B: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-({{x}^{3}}+1)$ C: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-{{x}^{2}}$ D: ${{\text{C}}_{1}}x+{{\text{C}}_{2}}{{e}^{x}}-{{x}^{2}}+1$

There are _____ texts. They are Text A _________________, Text B _________________, Text C _________________, Text D _________________.

There five texts in Chapter 6. Text A _________________________; Text B _______________________; Text C _______________________; Text C _______________________; Text E _______________________;

对数螺线$r={{\text{e}}^{\theta }}$在$\theta =\frac{\text{ }\!\!\pi\!\!\text{ }}{2}$对应点处的切线的直角坐标方程为( )。 A: $y+x={{\text{e}}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{2}}}$ B: $y-x={{\text{e}}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{2}}}$ C: $y={{\text{e}}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{2}}}(x+1)$ D: $y={{\text{e}}^{\frac{\text{ }\!\!\pi\!\!\text{ }}{2}}}(x-1)$

Part 1 ： The text begins with an _________.