Sketch the graph of the curve $y=\cos^2x\sin 2x$ for $0\leq x\leq\pi$, giving the exact coo

Question

Sketch the graph of the curve $y=\cos^2x\sin 2x$ for $0\leq x\leq\pi$, giving the exact coordinates of the points of intersection with the $x$-axis.[2] Find the exact coordinates of the maximum point. You do not have to show this is a maximum point.[4] Do not use a calculator in answering this part. Find the exact area bounded by the curve, the $x$-axis and the lines $x=0$ and $x=\dfrac{1}{4}\pi$.[4]

Accepted Answer

(a) Sketch with $x$-intercepts $(0,0)$, $\left(\dfrac{\pi}{2},0\right)$ and $(\pi,0)$ (b) $\left(\dfrac{\pi}{6},\dfrac{3\sqrt{3}}{8}\right)$ (c) $\dfrac{3}{8}$

N2026 P2 Q5

N2026 P2 Q5