Basic Analysis I — Real Analysis · Problem 5.1.8

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · riemann-integrability

Problem

Let

f : [a,b] \to \mathbb{R}

be a Riemann integrable function. Let

\alpha > 0

and

\beta \in \mathbb{R}

. Then define

g(x) := f(\alpha x + \beta)

on the interval

I = \left[\frac{a-\beta}{\alpha}, \frac{b-\beta}{\alpha}\right]

. Show that

g

is Riemann integrable on

I