5、用定积分表示y=x(x-1)(x-2)与x轴所围成的平面图形的面积

如果纯碎是求该图形的面积而不是该定积分的值的话,就要加上绝对值了,因为面积是大于0的.
令y = x(x - 1)(x - 2) = 0
--> x = 0、x = 1、x = 2
所以面积 = ∫[0→2] |y| dx
= ∫[0→2] |x(x - 1)(x - 2)| dx
= ∫[0→1] x(x - 1)(x - 2) dx - ∫[1→2] x(x - 1)(x - 2) dx
= {1/4} - {- 1/4}
= 1/2