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Compute the area enclosed between the curves y = sin x + cos x and y = |cos x - sin x| over the interval [0, pi/2].

1. 4*(sqrt(2) - 1)
2. 2*sqrt(2)*(sqrt(2) - 1)
3. 2*(sqrt(2) + 1)
4. 2*sqrt(2)*(sqrt(2) + 1)

Correct answer: 2*sqrt(2)*(sqrt(2) - 1)

Solution

The top curve sin x + cos x integrates to 2 over [0, pi/2]; |cos x - sin x| integrates to 2*(sqrt(2) - 1), so the area is 2 - 2*(sqrt(2)-1) = 2*sqrt(2)*(sqrt(2)-1)... evaluated to 2*sqrt(2)*(sqrt(2)-1).

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