The diagram depicts the curve $y = \sin^3 x\sqrt{\cos x}$ for $0 \leq x \leq \frac{\pi}{2}$, together with its highest point $M$.
(i)[6]
By using the substitution $u = \cos x$, determine by integration the exact area of the shaded region enclosed by the curve and the $x$-axis.
(ii)[6]
With all working shown, find the $x$-coordinate of $M$, giving your answer correct to $3$ decimal places.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or infer $du=-\sin x\,dx$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI