imo class 12 application of integrals

The area enclosed by the ellipse x²/a² + y²/b² = 1 is:

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The area enclosed by the ellipse x²/a² + y²/b² = 1 is:

  • A. πab
  • B. πa²
  • C. πb²
  • D. 2πab

Answer: A) πab

Explanation: Area of ellipse = 4 × ∫[0 to a] (b/a)√(a² − x²) dx = 4 × (b/a) × (πa²/4) = πab sq units.

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