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The area enclosed by the curves y = sin x + cos x and y = |cos x − sin x| over the interval [0, π/2] is -

1. 4(√2 − 1)
2. 2√2(√2 − 1)
3. 2√2(√2 + 1)
4. 2(√2 + 1)

Correct answer: 2√2(√2 − 1)

Solution

The area between the curves is calculated by integrating the difference between the upper and lower functions over the given interval. Here, y = sin x + cos x is the upper curve, and y = |cos x − sin x| is the lower curve. Solving the integral gives the result 2√2(√2 − 1).

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