The graph depicts the curve $y = \sin x \cos 2x$ over $0 \leq x \leq \frac{1}{2}\pi$, together with its maximum point $M$.
(a)[6]
Determine the $x$-coordinate of $M$, and give your answer correct to 3 significant figures.
(b)[5]
With the substitution $u = \cos x$, determine the area of the shaded region bounded by the curve and the $x$-axis in the first quadrant, and give your answer in its simplest exact form.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct product rule or chain rule.” …