imo class 12 definite integration

If ∫₀¹ (3x² + 2x + k) dx = 0, then k equals:

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If ∫₀¹ (3x² + 2x + k) dx = 0, then k equals:

  • A. −2
  • B. −1
  • C. 0
  • D. 1

Answer: A) −2

Explanation: ∫₀¹ (3x² + 2x + k) dx = [x³ + x² + kx]₀¹ = 1 + 1 + k = 2 + k = 0 → k = −2.

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