【答案】
分析:联解方程组,得直线与抛物线交于点A(-3,-6)和B(1,2),因此求出函数3-x
2-2x在区间[-3,1]上的定积分值,就等于所求阴影部分的面积,接下来利用积分计算公式和法则进行运算,即可得到本题的答案.
解答:![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/images0.png)
解:由
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/0.png)
,解得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/1.png)
或
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/2.png)
∴直线y=2x与抛物线y=3-x
2交于点A(-3,-6)和B(1,2)
∴两图象围成的阴影部分的面积为
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/3.png)
=(3×1-
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/4.png)
×1
3-1
2)-[3×(-3)-
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/5.png)
×(-3)
3-(-3)
2]
=
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131025123423438922692/SYS201310251234234389226006_DA/6.png)
,
故选:D
点评:本题求直线与抛物线围成的阴影部分图形的面积,着重考查了定积分计算公式和定积分的几何意义等知识,属于基础题.