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MHT CET202521 Apr 2025Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curve y =|x-2| between x=1, x=3 and X -axis is ......

Options

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

Correct answer

A. 1 sq.units

Step-by-step solution

The area bounded by y=|x-2| from x=1 to x=3 and the X-axis is found by evaluating ₁³ |x-2| dx . The piecewise definition of |x-2| gives two subintervals: [1,2] where |x-2|=2-x and [2,3] where |x-2|=x-2 . The integral splits accordingly: ₁³ |x-2| dx = ₁² (2-x) dx + ₂³ (x-2) dx Evaluating the first integral: ₁² (2-x) dx = [2x - x^2 2 ]₁² = (4-2) - (2 - 1 2 ) = 2 - 3 2 = 1 2 The second integral yields: ₂³ (x-2) dx = [ x^2 2 - 2x ]₂³ = ( 9 2 -6 ) - ( 4 2 -4 ) = - 3 2 + 2 = 1 2 The total area is 1 2 + 1 2 = 1 square uni

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