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