The area (in sq. units) of the region { x ∈ R :   x ≥ 0 ,  y ≥ 0 ,  y…

The area (in sq. units) of the region {x∈R: x≥0, y≥0, y≥x-2 and y≤x} is
  1. 133
  2.  83
  3.  103
  4.  53

Solution

y=x

x=x-2

(x)2-(x)-2=0

(x-2)(x+1)=0

x=2⇒x=4
Therefore, the area of the region is
∫04xdx- Area of ∆ABC

=23x3/2 04-12×2×2

=23×43/2-2
=163-2=103sq. unit

Asked in: JEE Main 2018 (15 Apr)

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