imo class 12 definite integration

Which of the following values is strictly greater?

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Which of the following values is strictly greater?

  • A. ∫[0 to 1] x dx
  • B. ∫[0 to 1] x² dx
  • C. Both are equal
  • D. Cannot be determined

Answer: A) ∫[0 to 1] x dx

Explanation: For x in (0, 1), x > x², so the area under x is strictly greater. Calculating: ∫[0 to 1] x dx = 1/2 and ∫[0 to 1] x² dx = 1/3.

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