f(a)g(x) dæ = f(£) / g(w) a a
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 f, g E R[a, b]. Suppose that g > 0 on [a, b].
1. Show that
inf f ·
[a,b)
| f(x)g(x) dæ < sup f
[a,b]
g(x) dæ <
g(x) dx.
a
2. Assume additionally that f E C[a,b]. Show that there is § E (a, b) such that
| f(x)g(x) dx = f(£) / g(x) dx.
Hint: use the intermediate value property for f.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda8e44cf-2e9e-4ce6-aa21-dc51ed340bd9%2Fbf4fad9c-f0d8-4980-86f9-e7b4944ee406%2Fu2strt_processed.png&w=3840&q=75)
Transcribed Image Text:Let f, g E R[a, b]. Suppose that g > 0 on [a, b].
1. Show that
inf f ·
[a,b)
| f(x)g(x) dæ < sup f
[a,b]
g(x) dæ <
g(x) dx.
a
2. Assume additionally that f E C[a,b]. Show that there is § E (a, b) such that
| f(x)g(x) dx = f(£) / g(x) dx.
Hint: use the intermediate value property for f.
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