<p>Evaluate \(\displaystyle\int_0^{\pi/2}\cos^6 x\,dx\) [JEE Main 2018]</p>
Step-by-Step Solution
Key Concept: Wallis: \int_0^(\pi/2) cos^6x dx = (5 \cdot 3 \cdot 1)/(6 \cdot 4 \cdot 2) \cdot (\pi/2) = 15/48 \cdot (\pi/2) = 5\pi/32.
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<p>Wallis (even power): $\int_0^{\pi/2}\cos^6 x\,dx = \frac{5\!\!}{6\!\!}\cdot\frac{\pi}{2}=\frac{5\cdot3\cdot1}{6\cdot4\cdot2}\cdot\frac{\pi}{2}=\frac{15}{48}\cdot\frac{\pi}{2}=\frac{5}{16}\cdot\frac{\pi}{2}=\frac{5\pi}{32}$</p>
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Correct Answer: A