Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK20269 May 2026Evening ShiftMathematicsArea Under CurvesActual

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5

Options

  1. A6.5 sq units
  2. B8.5 sq units
  3. C4.5 sq units
  4. D12.5 sq units

Correct answer

A. 6.5 sq units

Step-by-step solution

The required area is given by the definite integral of y = |2 - x| from x = 0 to x = 5 . A = ₀⁵ |2 - x| dx Since |2 - x| = 2 - x for x 2 and |2 - x| = x - 2 for x 2 , the integral is split at x = 2 . A = ₀² (2 - x) dx + ₂⁵ (x - 2) dx Evaluating the first integral: ₀² (2 - x) dx = [ 2x - x^2 2 ]₀² = (4 - 2) - 0 = 2 Evaluating the second integral: ₂⁵ (x - 2) dx = [ x^2 2 - 2x ]₂⁵ = ( 25 2 - 10 ) - (2 - 4) = 2.5 - (-2) = 4.5 Total area = 2 + 4.5 = 6.5 sq units. Answer: 6.5 sq units

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026The area of the region lying in the first quadrant and bounded by the curve y = 4x^2 , the Y-axis, and the lines y = 2 , y = 4 is... 2026 Full Area Under Curves list All COMEDK PYQs