Evaluate .

Answer and explanation

Correct answer: B.

  1. Step 1: The antiderivative of is . Evaluate: \left[-\frac{1}{2}\cos(2x) ight]_0^{\pi} = -\frac{1}{2}\cos(2\pi) - \left(-\frac{1}{2}\cos(0) ight) = -\frac{1}{2}(1) + \frac{1}{2}(1) = 0. **Answer: . Why not the others:** " half period" integrates over a quarter-period instead of the full cycle; " negative area" drops the positive compensating term from the lower limit; " full sine wave" confuses total absolute geometric area with the signed net definite integral.

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