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Evaluate the definite integral: integral from -pi/2 to pi/2 of (x*sin(x)) / (1 + e^x) dx.

1. pi²/4 - 2
2. pi²/4 + 2
3. 1
4. pi² - e^(pi/2)

Correct answer: 1

Solution

Adding f(x) and f(-x) collapses the exponential factor, leaving x*sin(x). Since x*sin(x) is even on a symmetric interval, the integral reduces to the integral of x*sin(x) from 0 to pi/2, which equals 1 by integration by parts.

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