22.A. Let g be defined on I = (0, 1] by 0 < * < }, 'I S* > { g(x) = 0, %3D 1, %3D Show that a bounded function f is integrable with respect to g on I if and only if f is continuous at į from the right and in this case, then f dg = f(}).
22.A. Let g be defined on I = (0, 1] by 0 < * < }, 'I S* > { g(x) = 0, %3D 1, %3D Show that a bounded function f is integrable with respect to g on I if and only if f is continuous at į from the right and in this case, then f dg = f(}).
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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22.A
![22.A. Let g be defined on I = (0, 1] by
0 < * < },
} < * < 1.
g (x) = 0,
1,
Show that a bounded function ƒ is integrable with respect to g on I if and only
if f is continuous at from the right and in this case,
then
f dg = f(}).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F826e2075-1af7-42d3-8aaa-603d35b31602%2F4dbbe5e2-ebd6-44bb-a713-06ff2e7621ab%2Fzypdd7d_processed.png&w=3840&q=75)
Transcribed Image Text:22.A. Let g be defined on I = (0, 1] by
0 < * < },
} < * < 1.
g (x) = 0,
1,
Show that a bounded function ƒ is integrable with respect to g on I if and only
if f is continuous at from the right and in this case,
then
f dg = f(}).
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