定积分求平面图形面积

(0，－3)处切线是y＝4x－3
(3，0)处切线是y＝6－2x
交点是(3/2，3)

面积S＝
∫0～3/2 [(4x－3)－(－x^2＋4x－3)]dx
＋
∫3/2～3 [(6－2x)－(－x^2＋4x－3)]dx
＝9/4

y'=-2x+4
(0,-3)处的切线y+3=4x
(3,0)处的切线y=-2(x-3)
两条切线的交点是(1.5,3)
所以面积=∫(0到1.5)[(4x-3)-(-x^2+4x-3)]dx+∫(1.5到3)[(-2(x-3))-(-x^2+4x-3)]dx
=∫(0到1.5)x^2dx+∫(1.5到3)(x-3)^2dx
=x^3/3(0到1.5)+(x-3)^3/3(1.5到3)
=9/4