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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Area Under Curves

NDA 2016 · Mathematics · Area Under Curves

Consider the curves y=|x-1| and |x|=2 What is the area of the...

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

Options

  1. A3 square units
  2. B4 square units
  3. C5 square units
  4. D6 square units

Correct answer

C. 5 square units

Step-by-step solution

Bounded region is shaded. So area of bounded region has two triangles ACBA C B and BDEB D E. Area of △ACB=12×3×3=92\triangle A C B=\frac{1}{2} \times 3 \times 3=\frac{9}{2} Area of △BDE=12×1×1=12\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 =△ACB+△BDE=92+12=5=\triangle A C B+\triangle B D E=\frac{9}{2}+\frac{1}{2}=5 square units
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