(i)[5]
Find the $x$-coordinate of $M$, and give your answer to 3 decimal places.
(ii)[4]
With the substitution $u = \sin x$ and all required working shown, determine the exact area of $R$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The graph depicts the curve $y = 5\sin^2 x\cos^3 x$ on $0 \leq x \leq \tfrac{1}{2}\pi$, together with its highest point $M$. The shaded area $R$ lies between the curve and the $x$-axis.