Let a : [0, 1] → R be defined as a(x) = = X x = [0, ₂) x + 1 x € [1,1]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let \( \alpha: [0, 1] \to \mathbb{R} \) be defined as
\[
\alpha(x) =
\begin{cases}
x & x \in [0, \frac{1}{2}) \\
x + 1 & x \in [\frac{1}{2}, 1]
\end{cases}
\]
Is \( f = \alpha \) Riemann-Stieltjes integrable with respect to \( \alpha \)? Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15ed467-90ec-4e60-afef-3d3f6119f74d%2F8e209732-b2d8-4129-8311-07cd503472a0%2F3ex1e3sm_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( \alpha: [0, 1] \to \mathbb{R} \) be defined as
\[
\alpha(x) =
\begin{cases}
x & x \in [0, \frac{1}{2}) \\
x + 1 & x \in [\frac{1}{2}, 1]
\end{cases}
\]
Is \( f = \alpha \) Riemann-Stieltjes integrable with respect to \( \alpha \)? Why?
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