来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/04/27 20:40:45
高数题,求曲线围成的面积
![](http://img.wesiedu.com/upload/8/d7/8d7fe03e8e0bea0783c88353ee0de907.jpg)
∫(0,1)|x(x-1)(2-x)|dx
+∫(1,2)|x(x-1)(2-x)|dx
=∫(0,1)x(x-1)(x-2)dx
+∫(1,2)x(x-1)(2-x)dx
=∫(0,1)(x³-3x²+2x)dx
-∫(1,2)(x³-3x²+2x)dx
=(x^4/4-x³+x²)|(0,1)-(x^4/4-x³+x²)|(1,2)
=1/4-1+1-0-[(4-8+4)-(1/4-1+1)]
=1/4+1/4
=1/2