The area between the curves y = sin x and y = cos x from x = 0 to x = π/2 is:
The area between the curves y = sin x and y = cos x from x = 0 to x = π/2 is:
- A. 2√2 − 2 sq units
- B. 2√2 sq units
- C. √2 − 1 sq units
- D. 2 − √2 sq units
Answer: A) 2√2 − 2 sq units
Explanation: Intersection at x = π/4. Area = ∫[0 to π/4] (cos x − sin x) dx + ∫[π/4 to π/2] (sin x − cos x) dx = [sin x + cos x]₀^(π/4) + [−cos x − sin x]_(π/4)^(π/2) = (√2/2+√2/2 − 1) + (−0−1 + √2/2+√2/2) = (√2 − 1) + (√2 − 1) = 2√2 − 2 sq units.
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