Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram illustrates the curve $y = \sin 2x \cos^2 x$ on $0 \leq x \leq \tfrac{1}{2}\pi$, together with its highest point $M$.

(a)[5]

With the substitution $u = \sin x$, determine the exact area of the region enclosed by the curve and the $x$-axis.

(b)[6]

Determine the exact $x$-coordinate of $M$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or imply that $du=\cos x\,dx$” …