imo class 12 definite integration

If ∫₀ᵃ √x dx = 18, then a equals:

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If ∫₀ᵃ √x dx = 18, then a equals:

  • A. 6
  • B. 9
  • C. 12
  • D. 36

Answer: B) 9

Explanation: ∫₀ᵃ x^(1/2) dx = [ (2/3) x^(3/2) ]₀ᵃ = (2/3) a^(3/2) = 18 → a^(3/2) = 27 → √a³ = 27 → a³ = 729 → a = 9.

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