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The graphs of y = sin x and y = cos x meet at infinitely many points, forming repeated bounded regions of equal area. The area of one such region is

1. √2
2. 2√2
3. 3√2
4. 4√2

Correct answer: 2√2

Solution

Consecutive intersections at x=pi/4 and x=5pi/4. Area = Integral |sin x - cos x| dx from pi/4 to 5pi/4 = 2*sqrt(2).

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