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