imo class 12 definite integration

Find the value of ∫[1 to 4] |x - 2| dx.

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Find the value of ∫[1 to 4] |x - 2| dx.

  • A. 2
  • B. 5/2
  • C. 3
  • D. 7/2

Answer: B) 5/2

Explanation: Split the integral at x = 2: ∫[1 to 2] (2 - x) dx + ∫[2 to 4] (x - 2) dx. = [2x - x²/2] from 1 to 2 + [x²/2 - 2x] from 2 to 4. = (4 - 2 - (2 - 1/2)) + ((8 - 8) - (2 - 4)) = 1/2 + 2 = 5/2.

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