Mathematics

Mathematics

Problem

Which definite integral equals lim⁡n→∞∑i=1nπ2n cos⁡ ⁣(πi2n) \displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}\frac{\pi}{2n}\,\cos\!\Bigl(\frac{\pi i}{2n}\Bigr)\, ? a) ∫0πcos⁡x dx\displaystyle \int_{0}^{\pi} \cos x\,dx b) ∫0π/2sin⁡x dx\displaystyle \int_{0}^{\pi/2} \sin x\,dx c) ∫0π/2cos⁡x dx\displaystyle \int_{0}^{\pi/2} \cos x\,dx d) ∫π/2πcos⁡x dx\displaystyle \int_{\pi/2}^{\pi} \cos x\,dx

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