Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram displays the graph of $y = 5\sin 2x\cos^2 x$ for $0 \leq x \leq \tfrac{1}{2}\pi$ and its maximum point $M$.
(a)[6]

Find the exact $x$-coordinate corresponding to $M$.

(b)[5]

Using the substitution $u = \cos x$, determine the area of the region enclosed by the curve, the $x$-axis between $x = 0$ and $x = \tfrac{1}{4}\pi$, and the line $x = \tfrac{1}{4}\pi$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate $\cos^2x$ and get $-2\sin x\cos x$

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