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NDA 2 2024 Maths, question 91

Topic: Integral calculus

Passage · Q91 to Q92

Let f(x)=∣x2−x−2∣f(x)=|x^{2}-x-2|.

Q91

What is ∫02f(x)dx\int _{0}^{2}f(x) dx equal to?

  1. (a) 00
  2. (b) 11
  3. (c) 5/35/3
  4. (d) 10/310/3Correct answer

Solution.

Answer: (d) 10/310/3

  1. Factor x²−x−2=(x−2)(x+1).
  2. On [0,2] it is nonpositive, so f(x)=−x²+x+2.
  3. The integral is [−x³/3+x²/2+2x]₀²=−8/3+2+4=10/3.