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NDA 2 2025 Maths, question 74

Topic: Integral calculus

Passage · Q73 to Q75

Consider the function f(x)=x∣x∣f(x)=x|x|.

Q74

What is the area bounded by the curve f(x)f(x), the xx-axis and the lines x=−2x=-2 and x=1x=1?

  1. (a) 13\frac{1}{3}
  2. (b) 23\frac{2}{3}
  3. (c) 52\frac{5}{2}
  4. (d) 33Correct answer

Solution.

Answer: (d) 33

  1. Geometric area integrates |f(x)|=x².
  2. Thus the area is ∫ from −2 to 0 of x² dx plus ∫ from 0 to 1 of x² dx, equal to 8/3+1/3=3.
  3. Using the signed integral of f would incorrectly subtract the left-hand area.