imo class 12 application of integrals

The area of the region bounded by y = x² + 1, y = x, x = 0 and x = 2 is:

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The area of the region bounded by y = x² + 1, y = x, x = 0 and x = 2 is:

  • A. 4/3 sq units
  • B. 8/3 sq units
  • C. 2/3 sq units
  • D. 10/3 sq units

Answer: A) 4/3 sq units

Explanation: Area = ∫[0 to 2] ((x² + 1) − x) dx = [x³/3 + x − x²/2]₀² = 8/3 + 2 − 2 = 8/3 sq units.

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