The area bounded by the curve y = sin² x, the x-axis and the lines x = 0 and x = π is: A. π/2 sq units B. π sq units C. π/4 sq units D. 2π sq units Answer: A) π/2 sq units Explanation: Area = ∫[0 to π] sin² x dx = ∫[0 to π] (1 − cos 2x)/2 dx = (1/2)[x − (sin 2x)/2]₀^π = (1/2)(π − 0) = π/2 sq units.

imo class 12 application of integrals

The area bounded by the curve y = sin² x, the x-axis and the lines x = 0 and x = π is:

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The area bounded by the curve y = sin² x, the x-axis and the lines x = 0 and x = π is:

Answer: A) π/2 sq units

Explanation: Area = ∫[0 to π] sin² x dx = ∫[0 to π] (1 − cos 2x)/2 dx = (1/2)[x − (sin 2x)/2]₀^π = (1/2)(π − 0) = π/2 sq units.