The value of \(\int_{0}^{\pi}\displaystyle \cos^{2}x\,dx\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{\pi}{2}\)
By the double-angle identity \(\cos 2x = 2\cos^{2}x - 1\),
\( \displaystyle \cos^{2}x = \frac{1 + \cos 2x}{2} \)
So
\( \displaystyle \int_{0}^{\pi}\cos^{2}x\,dx = \Big[\frac{x}{2} + \frac{\sin 2x}{4}\Big]_{0}^{\pi} \)
\( \displaystyle = \left(\frac{\pi}{2} + 0\right) - (0 + 0) \)
\( \displaystyle = \frac{\pi}{2} \)