Q183 / 270 · NDA 2016 (Phase 1) · Mathematics

Consider the curves $y=|x-1|$ and $|x|=2$ What is the area of the region bounded by the curves and x-axis?

  • A
    3 square units
  • B
    4 square units
  • Correct answer
    C
    5 square units
  • D
    6 square units

Solution

Bounded region is shaded. So area of bounded region has two triangles $A C B$ and $B D E$. Area of $\triangle A C B=\frac{1}{2} \times 3 \times 3=\frac{9}{2}$ Area of $\triangle B D E=\frac{1}{2} \times 1 \times 1=\frac{1}{2}$ Area of region bounded by curves and x -axis is Area $=\triangle A C B+\triangle B D E=\frac{9}{2}+\frac{1}{2}=5$ square units

Hence, the correct answer is option: 'C'.

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