The area of the region bounded by y = √(x − 1), x = 2, x = 5 and y = 0 is: A. 14/3 sq units B. 16/3 sq units C. 8/3 sq units D. 10/3 sq units Answer: A) 14/3 sq units Explanation: Area = ∫[2 to 5] √(x − 1) dx = ∫[1 to 4] √t dt (t = x−1) = [t^(3/2) / (3/2)]₁⁴ = (2/3)(8 − 1) = 14/3 sq units.

imo class 12 application of integrals

The area of the region bounded by y = √(x − 1), x = 2, x = 5 and y = 0 is:

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The area of the region bounded by y = √(x − 1), x = 2, x = 5 and y = 0 is:

Answer: A) 14/3 sq units

Explanation: Area = ∫[2 to 5] √(x − 1) dx = ∫[1 to 4] √t dt (t = x−1) = [t^(3/2) / (3/2)]₁⁴ = (2/3)(8 − 1) = 14/3 sq units.