Shaded area has to be calculated Curve 1: y = |x - 1| ⇒ y = 1 - x for x < 1 ⇒ y = x - 1 for x ≥ 1 Curve 2: y = 3 - |x| ⇒ y = 3 + x for x < 0 ⇒ y = 3 - x for x ≥ 0
Area enclosed (A)=
x2
∫
x1
(y1−y2)dx ⇒A=
2
∫
−1
3−|x|−|x−1|dx ⇒A=|
0
∫
−1
3+x−(1−x)dx|+|
1
∫
0
3−x−(1−x)dx|+|
2
∫
1
3−x−(x−1)dx| ⇒A=|
0
∫
−1
(2+2x)dx|+|
1
∫
0
2dx|+|
2
∫
1
(4−2x)dx| ⇒A=|[2x+x2]−10|+|[2x]01|+|[4x−x2]12| ⇒A=1+2+1=4sq. units