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Evaluate the definite integral ∫₀^(π/2) |sin x - cos x| dx.

1. 2√(2)
2. 2(√(2)-1)
3. √(2)+1
4. None of these

Correct answer: 2(√(2)-1)

Solution

For 0..pi/4, cos>sin; for pi/4..pi/2, sin>cos. Integral = Integral(cos-sin) from 0 to pi/4 + Integral(sin-cos) from pi/4 to pi/2 = (sqrt2-1)+(sqrt2-1) = 2(sqrt2-1).

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