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NDA2025MathematicsArea Under CurvesActual

What is the area of the region bounded by |x| 2k and |y| k , where k is a positive real number?

Options

  1. A2k^2
  2. B4k^2
  3. C5k^2
  4. D8k^2

Correct answer

D. 8k^2

Step-by-step solution

The given inequalities are |x| 2k and |y| k . This can be written as -2k x 2k and -k y k . These inequalities represent a rectangular region in the xy -plane. The length of the rectangle along the x -axis is 2k - (-2k) = 4k . The width of the rectangle along the y -axis is k - (-k) = 2k . The area of the rectangular region is given by length width. Area = 4k 2k = 8k^2 . Answer: 8k^2

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