Definite integral

1.Findthe value of c that satisfies the integral equation∫(0 to c) ｜x^2－1｜dx = c
(Assume that c>0)
Sol
∫(0 to c)_｜x^2－1｜dx
(1) 1>c>0
∫(0 to c)_｜x^2－1｜dx
=∫(0 to c)_1－x^2dx
=x－x^3/3|(0 to c)
=c^3/3－c=c
c^3/3=2c
c^2=6(reject)
(2) c>1
∫(0 to c)_｜x^2－1｜dx
=∫(0 to 1)_｜x^2－1｜dx+∫(1 to c)_｜x^2－1｜dx
=∫(0 to 1)_1－x^2dx+∫(1 to c)_x^2－1dx
=x－x^3/3｜(0 to 1)+(x^3/3－x)｜(1 to c)
=[(1－1/3)－0]+[(c^3/3－c)－(1/3－1)]
=2/3+c^3/3－c+2/3=c
2+c^3－3c+2=3c
c^3－6c+4=0
(c－2)(c^2+2c－2)=0
c=2 or c=(－2+/-√12))/2(reject)

抱歉 可能我還未能理解,,,,
我需要時間消化一下,,,
就請別的解答一下吧...

需考慮 c >= 1 和 c < 1 兩 case.

0.732 可能不適合,請對一下.