Evaluate the integral using integration by parts.
Answer and explanation
Correct answer: B. obtained via parts formula
- Step 1: Integration by parts: . Let , and . \int_0^{\pi/2} x \cos x \, dx = [x \sin x]_0^{\pi/2} - \int_0^{\pi/2} \sin x \, dx = \left(\frac{\pi}{2} \cdot 1 - 0 ight) - [-\cos x]_0^{\pi/2} = \frac{\pi}{2} - (0 - (-1)) = \frac{\pi}{2} - 1. **Answer: obtained via parts formula. Why not the others:** " sign error" makes a sign error in evaluating the cosine integral limit ; " missing boundary term" neglects the boundary evaluation ; " doubled result" arbitrarily doubles the integral outcome during computation.
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