Determine the area bounded by the curves y = cos(x) and y = sin(x) between x = 0 and x = π/4. A. √2 − 1 B. √2 C. 1 D. 1 − 1/√2 Answer: A) √2 − 1 Explanation: In [0, π/4], cos(x) ≥ sin(x). Area = ∫(0 to π/4) (cos(x) − sin(x)) dx = [sin(x) + cos(x)] = (1/√2 + 1/√2) − (0 + 1) = √2 − 1.

imo class 12 application of integrals

Determine the area bounded by the curves y = cos(x) and y = sin(x) between x = 0 and x = π/4.

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Determine the area bounded by the curves y = cos(x) and y = sin(x) between x = 0 and x = π/4.

Answer: A) √2 − 1

Explanation: In [0, π/4], cos(x) ≥ sin(x). Area = ∫(0 to π/4) (cos(x) − sin(x)) dx = [sin(x) + cos(x)] = (1/√2 + 1/√2) − (0 + 1) = √2 − 1.