EDB — 1B0

Exercises

1. [1B0]Prerequisites:Fundamental theorem of integral calculus.

   Suppose that \(f:[a,b]→ℝ\) is continuous and \(g:ℝ→ℝ\) has class \(C^ 1\): prove that

   \[ ∫_ a^ b f(g(t)) g'(t) \, {\mathbb {d}}t = ∫_{g(a)}^{g(b)} f(s) \, {\mathbb {d}}s \quad . \]
   Solution 1

   [1B2]↺↻

   Note that for this result it is not necessary to assume that \(g\) is monotonic.