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Evaluate the definite integral ∫_(-π/2)^(π/2) (sin² x)/(1+2^x) dx.

1. π/2
2. 4π
3. π/4
4. π/8

Correct answer: π/4

Solution

The integral evaluates to frac{ ext{Area under the curve of } rac{ ext{sin}² x}{1+2^x}}{ ext{symmetry and properties of definite integrals}} over the interval from - rac{ ext{pi}}{2} to rac{ ext{pi}}{2}, resulting in frac{ ext{pi}}{4}.

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