The diagram shows the curve $y = \frac{1}{2}(\cos 2x + 2\cos x + 1)$ for $0 \le x \le \pi$

Question

The diagram shows the curve $y = \frac{1}{2}(\cos 2x + 2\cos x + 1)$ for $0 \le x \le \pi$ radians. The point $M$ is the minimum point of the curve, where the $x$-coordinate of $M$ lies in the interval $\frac{\pi}{2} < x < \pi$. Find the exact coordinates of $M$.[5] Find the exact total area of the shaded region bounded by the curve and the axes.[4]

Accepted Answer

(a) $M=\left(\frac{2\pi}{3},-\frac{1}{4}\right)$ (b) $2\text{ units}^2$

(A Math) 2025 CCHY PRELIMS P2 Q7

(A Math) 2025 CCHY PRELIMS P2 Q7

Solution:

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