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NDA 2019 Maths · Mathematics · Application of Integrals · medium

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

Single correct option

The area of the region bounded by the graph of y=∣x−1∣y=|x-1| and the line y=3y=3 is
  1. A. 66 sq. units
  2. B. 92\frac92 sq. units
  3. C. 1212 sq. units
  4. D. 99 sq. units
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Answer: (D) 99 sq. units

The graph y=∣x−1∣y=|x-1| meets y=3y=3 where ∣x−1∣=3|x-1|=3, i.e. at x=−2x=-2 and x=4x=4. The enclosed region is a triangle with base 66 (from −2-2 to 44) and height 33 (apex at (1,0)(1,0)), so the area is 12⋅6⋅3=9\frac12\cdot6\cdot3=9. The value 92\frac92 is half this and corresponds to only one of the two halves of the region.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake