2.79: Product rule, normal and integration

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$.

Find the equation of the normal to the curve at the point where $x = \pi$, giving your answer in the form $y = mx + c$.

Using your answer to part (a), find the exact value of $\displaystyle\int_{0}^{\pi/6} x\sin x\,\mathrm{d}x$.