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Manipal MET2022MathematicsArea Under Curves

The area of the region bounded by the curves y=|x-2|, x=1, x=3 and the x -axis is

Options

  1. A1 sq unit
  2. B2 sq units
  3. C3 sq units
  4. D4 sq units

Correct answer

A. 1 sq unit

Step-by-step solution

aligned Required area & = ₁^3 y d x & = ₁^3|x-2| d x & = ₁^2-(x-2) d x+ ₂^3(x-2) d x & = ₁^2(2-x) d x+ ₂^3(x-2) d x = & [2 x- x^2 2 ]₁^2+ [ x^2 2 -2 x ]₂^3 = & [4-2- (2- 1 2 ) ]+ [ 9 2 -6-(2-4) ] = & 2- 3 2 - 3 2 +2 = & 1 sq unit aligned

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