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Let A1 be the area of the region bounded by the curves y=sin x, y=cos x and y-axis in the first quadrant. Let A2 be the area of the region bounded by the curves y=sin x, y=cos x, x-axis and x=π/2 in the first quadrant. Then,
- A₁:A₂=1:√(2) and A₁+A₂=1
- A₁=A₂ and A₁+A₂=√(2)
- 2A₁=A₂ and A₁+A₂=1+√(2)
- A₁:A₂=1:2 and A₁+A₂=1
Correct answer: A₁:A₂=1:√(2) and A₁+A₂=1
Solution
The correct option states that the ratio of areas A1 and A2 is 1 to √2, which reflects the geometric relationship between the curves in the specified regions, and that their sum equals 1, indicating that the total area under consideration is normalized to a unit area.
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