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MHT CET202620 April 2026Morning ShiftMathematicsArea Under CurvesActual

The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is

Options

  1. A1 sq.unit
  2. B2 sq. units
  3. C2 2 sq.units
  4. D4 sq.units

Correct answer

B. 2 sq. units

Step-by-step solution

The given curves are y = |x| - 1 and y = -|x| + 1 . To find the points of intersection, we equate the two equations: |x| - 1 = -|x| + 1 2|x| = 2 |x| = 1 x = 1 The required area A is the region bounded between these two curves from x = -1 to x = 1 . A = _ -1 ¹ [(-|x| + 1) - (|x| - 1)] dx A = _ -1 ¹ (2 - 2|x|) dx Since the integrand is an even function: A = 2 ₀¹ (2 - 2x) dx A = 2 [ 2x - x^2 ]₀¹ A = 2 (2 - 1) = 2 sq. units. Answer: 2 sq. units

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