图中所示的是曲线 $y=x^2-12x+37$ 和直线 $y=-4x+30$。

求阴影区域的面积。

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。

联立直线和曲线求积分端点。图中直线在上，面积是两者纵坐标之差的定积分。

The intersection equation is $x^2-8x+7=(x-1)(x-7)=0$, giving $x=1,7$. Between these values the line lies above the curve. The shaded area is

也可以先用梯形公式求直线下方的面积，再减去同一区间内曲线下方的面积。

The endpoints of the straight edge are $(1,26)$ and $(7,2)$. The area under the line on this interval is $\frac12(26+2)(7-1)=84$. The parabola is $(x-6)^2+1>0$, and the area under it is

The difference is $84-48=36$.