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NDA 1 2025 Maths, question 86

Topic: Integral calculus

Passage · Q85 to Q86

Let the curve f(x)=∣x−3∣f(x) = |x - 3|.

Q86

What is the area bounded by the curve f(x)f(x) and y=3y = 3?

  1. (a) 3 square units
  2. (b) 4.5 square units
  3. (c) 7.5 square units
  4. (d) 9 square unitsCorrect answer

Solution.

Answer: (d) 9 square units

  1. The intersections satisfy ∣x−3∣=3|x - 3| = 3, giving x=0x = 0 and x=6x = 6.
  2. The enclosed region is a triangle with base 6 and height 3.
  3. Its area is 12×6×3=9\frac{1}{2} \times 6 \times 3 = 9 square units.