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NDA 2 2024 Maths, question 92

Topic: Integral calculus

Passage · Q91 to Q92

Let f(x)=∣x2−x−2∣f(x)=|x^{2}-x-2|.

Q92

What is ∫13f(x)dx\int _{1}^{3}f(x) dx equal to?

  1. (a) 22
  2. (b) 33Correct answer
  3. (c) 44
  4. (d) 55

Solution.

Answer: (b) 33

  1. The sign changes at x=2.
  2. Therefore split the area: ∫₁²(−x²+x+2)dx+∫₂³(x²−x−2)dx.
  3. The two contributions are 7/6 and 11/6, giving 3.