Exercise 11.8

Question

If $f \in \mathscr{R}$ on $[a,b]$ and if $F(x) = \int_a^x f(t)\,dt$, prove that $F'(x) = f(x)$ almost everywhere on $[a,b]$.

Amit Awasthi · Accepted Answer

\begin{proof}
      This follows by Theorem $11.33$ since $f$ is continuous almost everywhere
      on $[a,b]$, so by Theorem $6.20$, $F$ is differentiable almost everywhere,
      and $F'(x) = f(x)$ at those points.
\end{proof}

Exercise 11.8

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Exercise 11.8

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