Question: Let (f:[0, infty) ightarrow mathbb{R}) be absolutely continuous. Show that (int f^{a-1} d f=f^{a} / a) for all (a>0).

Let \(f:[0, \infty) ightarrow \mathbb{R}\) be absolutely continuous. Show that \(\int f^{a-1} d f=f^{a} / a\) for all \(a>0\).

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