The function \(f\) is defined by \(f(x)=\frac1{\sqrt{9-x^2}}\), where \(-3<x<3\).
Find \(\displaystyle\int f(x)\,\mathrm dx\).[1]
Find the first four non-zero terms in the binomial expansion of \(f(x)\) in ascending powers of \(x\), giving each coefficient as an exact fraction.[4]
Hence find the first four non-zero terms in the Maclaurin series for \(\sin^{-1}(\frac13x)\), giving each coefficient as an exact fraction.[4]