Answer
$$x = 10\sin \theta $$
Work Step by Step
$$\eqalign{
& {\text{The integral }}\sqrt {100 - {x^2}} {\text{ contains }}{a^2} - {x^2},{\text{ then the change of }} \cr
& {\text{variables suggested is}}:\,\,x = a\sin \theta \cr
& {\text{Let }}a = 10,{\text{ then}} \cr
& x = 10\sin \theta \cr} $$
