imo class 12 application of integrals

The area of the region bounded by y = √(x − 1), y = 0 and x = 2 is:

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The area of the region bounded by y = √(x − 1), y = 0 and x = 2 is:

  • A. 2/3 sq unit
  • B. 1/3 sq unit
  • C. 4/3 sq units
  • D. 1 sq unit

Answer: A) 2/3 sq unit

Explanation: Area = ∫[1 to 2] √(x − 1) dx = ∫[0 to 1] √t dt = (2/3)[t^(3/2)]₀¹ = 2/3 sq unit.

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