Exercise 8.1.14

Question

\begin{enumerate}[label=(\alph*)] 
\item Why are we sure that $f$ and $(F \circ g)'$ have generalized Riemann integrals?
\item Use Theorem 8.1.9 to finish the proof.
 \end{enumerate}

Ulisse Mini · Accepted Answer

\begin{enumerate}[label=(\alph*)] 
\item Both of them are derivatives of some function.
\item
$$
\int^b_a (f \circ g) \cdot g' = \int^b_a (F \circ g)' = (F \circ g)(b) - (F \circ g)(a) = F(g(b)) - F(g(a)) = \int^{g(b)}_{g(a)} f
$$
 \end{enumerate}

Exercise 8.1.14

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Exercise 8.1.14

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