UPSC NDA Math Model Paper 6

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