图中所示为方程为 $y=(3x-2)^{\frac12}$ 的曲线和直线 $y=\frac12x+1$。曲线与直线交于点 $A$ 和 $B$。

(a) 求 $A$ 和 $B$ 的坐标。

(b) 由此求曲线与直线之间所围区域的面积。

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。

令两曲线的纵坐标相等并平方。求根后回代原根式方程。

The equation $\sqrt{3x-2}=x/2+1$ gives

At $x=2$ the original heights are both $2$, and at $x=6$ both are $4$. From the diagram, $A=(2,2)$ and $B=(6,4)$.

用交点作积分端点。根式曲线在上，积分时减去直线的纵坐标。

The area is

也可先算直线下方的梯形面积，再从曲线下方的面积中扣除它。

The line between $A$ and $B$ is above a trapezium of area $(2+4)(6-2)/2=12$. The area under the root curve is

The required difference is $4/9$.