Question

求曲线y=x平方-1与y=x＋1所围成的图像面积

Answer 1

y=x²培世察-1=x+1
x²-x-2=0
x=-1,x=2
而-1<x<2时,x²-1<配茄x+1
所以面积S=∫(-1到2)[(x+1)-(x²返早-1)]dx
=∫(-1到2)(-x²+x+2)dx
=(-x³/3+x²/2+2x)(-1到2)
=(-8/3+2+4)-(1/3+1/2-2)
=9/2

Answer 2

先求出交点，再如下计算
∫圆桥[x+1-(x²-1)]dx
=∫(x+1-x²+1)dx
=∫(x+2-x²)dx
=x²/2+2x-x³/3(-1,2)
=2²/2+2*2-2³/3-[(-1)²/2+2*(-1)-(-1)³世困/3]
=2+4-8/3-(1/2-2+1/3)
=6-8/3-(1/2-2+1/搜腔念3)
=6-8/3-1/2+2-1/3
=6-3-1/2+2
=5-1/2
=4.5

Answer 3

把闷链图像画出来液罩肢。
找闹世出边界点。

等于 ∫ [（x+1)-(x²-1)] dx