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JEE Main2003MathematicsArea Under CurvesActual

The area of the region bounded by the curves y=|x-1| and y=3-|x| is

Options

  1. A6 sq. units
  2. B2 sq. units
  3. C3 sq. units
  4. D4 sq. units

Correct answer

D. 4 sq. units

Step-by-step solution

A= _ -1 ^0 (3+x)-(-x+1) d x+ ₀^1 (3-x)-(-x+1) d x+ ₁^2 (3-x)-(-x-1) d x= _ -1 ^0(2+2 x) d x+ ₀^1 2 d x+ ₁^2(4-2 x) d x= [2 x-x^2 ]_ -1 ^0+[2 x]₀^1+ [4 x-x^2 ]₁^2=0-(-2+1)+(2-0)+(8-4)-(4-1)=1+2+4-3=4 sq. units

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