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The value of ∫[0 to π/2] (sin³ x)/(sin x + cos x) dx is:

1. (π - 2)/8
2. (π - 1)/4
3. (π - 2)/4
4. (π - 1)/2

Correct answer: (π - 1)/4

Solution

The integral evaluates to (π - 1)/4 due to the symmetry and periodic properties of the sine and cosine functions, which allows for simplification and substitution that leads to this specific result.

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