imo class 12 application of integrals

If the area of the region bounded by y = ax² (where a > 0), the x-axis, and x = 1 is exactly 1 square unit, what is the value of 'a'?

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If the area of the region bounded by y = ax² (where a > 0), the x-axis, and x = 1 is exactly 1 square unit, what is the value of 'a'?

  • A. 3
  • B. 1
  • C. 2
  • D. 1/3

Answer: A) 3

Explanation: Area = ∫(0 to 1) ax² dx = [ax³/3] from 0 to 1 = a/3. Setting a/3 = 1 gives a = 3.

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