Solution
= Solution
For $\phi(t)=re^{it}$, $\phi'(t)=ire^{it}$ and $|\phi'(t)|=r$. The <triangle inequality for an integral> applied to the parametrized <contour integral> gives
$$
\boxed{\left|\int_\phi f(z)\,dz\right|=\left|\int_0^{2\pi}f(re^{it})ire^{it}\,dt\right|\leq r\int_0^{2\pi}|f(re^{it})|\,dt.}
$$
This is the circular-contour instance of the <estimation lemma>.