Combine inverse-sine integration with two rotation radii

(a) Find $\int\sin^{-1}(3x)\,dx$.3 marks

(b) The curves $C_1,C_2$ are $y=1-(\sqrt3/\pi)x^2$ and $y=\tfrac13\cos x$. Rotate the first-quadrant region bounded by them and the y-axis through $360^\circ$ about the y-axis. Find the volume to 2 decimal places.4 marks