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The graphs of y = sin x and y = cos x intersect repeatedly, and between two consecutive intersection points they enclose equal regions, each of area A. Find the value of A⁴.
- 16
- 64
- 32
- 8
Correct answer: 64
Solution
A = int_(pi/4)^(5pi/4) (sin x - cos x) dx = 2 sqrt(2), so A⁴ = (2 sqrt 2)⁴ = 64.
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