Exercises
[1B0]Prerequisites:Fundamental theorem of integral calculus.
Suppose that \(f:[a,b]ββ\) is continuous and \(g:βββ\) has class \(C^ 1\): prove that
\[ β«_ a^ b f(g(t)) g'(t) \, {\mathbb {d}}t = β«_{g(a)}^{g(b)} f(s) \, {\mathbb {d}}s \quad . \]1