imo class 12 definite integration

If ∫₀ᵏ (2x + 3) dx = 10, then k equals:

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If ∫₀ᵏ (2x + 3) dx = 10, then k equals:

  • A. 2
  • B. 3
  • C. 4
  • D. 1

Answer: A) 2

Explanation: ∫₀ᵏ (2x+3) dx = [x² + 3x]₀ᵏ = k² + 3k = 10 → k² + 3k − 10 = 0 → (k+5)(k−2) = 0 → k = 2 (positive).

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