Evaluate : \(\int_0^{\pi/2} \cos^2 x \, dx\)
Q.11 Evaluate : \(\int_0^{\pi/2} \cos^2 x \, dx\)
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Answer: \(\frac{\pi}{4}\)
\(\int_0^{\pi/2} \cos^2 x\,dx = \frac{1}{2}\int_0^{\pi/2} (1 + \cos 2x)\,dx = \frac{1}{2}\left[x + \frac{\sin 2x}{2}\right]_0^{\pi/2}\)
\(= \frac{1}{2}\left[\left(\frac{\pi}{2} + \frac{\sin\pi}{2}\right) - (0 + 0)\right] = \frac{1}{2} \cdot \frac{\pi}{2} = \frac{\pi}{4}\).
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· 29 Oct 2026
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