imo class 12 definite integration

Find the value of ∫[1 to 2] (x² - 1)/x² dx.

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Find the value of ∫[1 to 2] (x² - 1)/x² dx.

  • A. 1/2
  • B. 1
  • C. 3/2
  • D. 5/2

Answer: A) 1/2

Explanation: Divide the terms: ∫ (1 - x⁻²) dx. Anti-derivative is x + 1/x. Evaluating from 1 to 2: (2 + 1/2) - (1 + 1) = 5/2 - 2 = 1/2.

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