I want to convert the integral defined below on $|y|=r$ in $\mathbb{R}^3$ to unit sphere. I changed variable $y=rw$
\begin{align} \int_{|y|=r} \Phi(x,y)ds(y)= \int_{|w|=1} \Phi(x,rw)ds(rw) \end{align} I want to find the jacobian . I dont undestand what $ds(rw )$ means. can we write it in detail ? I mean as meaning of $ds(rw)$. Thank you for your help.