Find the area between the curves y=|x-1| and
y= -|x-1|+1

Answer :

Firs we form a table for different value of x and y for both equation , As :
 

y  = | x - 1 |		y  = - | x - 1 | + 1
x	y	x	y
0	1	0	0
0.5	0.5	0.5	0.5
1	0	1	1
1.5	0.5	1.5	0.5
2	1	2	0
-0.5	1.5	-0.5	-0.5

Now we represent these points on x  -  y , plane , As :

Here Length of AC  =  1 unit and Distance ( Height ) between vertices D and line AC  = 0.5 unit  and between vertices B and line AC  = 0.5 unit 

We know Area of triangle = $\frac{1}{2}\times Base \times Height$
So,
Area of triangle ABC  =  Area of triangle ADC  ,
And
Area of triangle ABC  = $\frac{1}{2}\times AC \times \frac{1}{2} = \frac{1}{2}\times 1 \times \frac{1}{2} = \frac{1}{4} = 0.25 uni{t}^2$
And
Area of triangle ADC  = 0.25 unit²
So,
Area of required ABCD  = 0.25  + 0.25  = 0.50 unit²                               ( Ans )