AMU Engineering 2019 solved paper Solved Paper

Given that, y=|x−1| ......(i)
and y=3−|x| ........(ii)
Solving the Eqs. (i) and (ii)
if x≥1, then 3−x=x−1⇒x=2
if 0≤x≤1, then 3−x=1−x
(which is not possible)
Also, if x<0, then 3+x=1−x⇒x=−1
Thus, required area
=

2

∫

−1

(3−|x|−|x−1|)dx
=

0

∫

−1

[3+x−(1−x)]dx +

1

∫

0

[(3−x)−(1−x)]dx +

2

∫

1

[(3−x)−(x−1)]dx
=

0

∫

−1

(2+2x)dx+2‌

1

∫

0

1dx+

2

∫

1

(4−2x)dx
=[2x+x2]−10+[4x−x2]12
=1+2+1=4 sq units