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If ∫₀^(π) x f(sin x) dx = A ∫₀^(π/2) f(sin x) dx, then the value of A is

1. 2π
2. π
3. π/4
4. 0

Correct answer: π

Solution

The integral on the left can be simplified using the symmetry of the sine function and the properties of definite integrals, leading to the conclusion that the factor A must equal C0 to balance the two sides.

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