(i)[5]
Show that the normal at $Q$ passes through the point $(\pi, 0)$.
(ii)[2]
Find the value of $\frac{d}{dx}(\sin x - x \cos x)$.
(iii)[3]
Hence evaluate the integral $\int_0^{\frac{1}{2}\pi} x \sin x \, dx$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram depicts the curve $y = x \sin x$, for $0 \leq x \leq \pi$. The point $Q\left(\frac{1}{2}\pi, \frac{1}{2}\pi\right)$ is on the curve.