图中显示方程为 $x=y^2+1$ 的曲线。点 $A(5,2)$ 和 $B(2,-1)$ 位于曲线上。

(a) 求直线 $AB$ 的方程。

(b) 将曲线与直线 $AB$ 之间的区域绕 $y$ 轴旋转 $360^\circ$，求所得旋转体的体积。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

用两点求斜率，再代入任一点确定直线方程。

The gradient of $AB$ is $(2-(-1))/(5-2)=1$. Through $(5,2)$, the line is $y-2=x-5$, or $y=x-3$.

绕 $y$ 轴旋转时取水平截面。外半径来自直线，内半径来自抛物线，体积要积分两个半径的平方差。

For $-1\le y\le2$, the outer radius is $y+3$ and the inner radius is $y^2+1$. The radii are positive, and the outer one is at least as large since $y+3-(y^2+1)=(2-y)(y+1)\ge0$. The volume is