(b) Let A € D(RP) and suppose f and g are integrable on A. Let g(x) ≥ 0 for all x € A. If m = inf f(A) and M sup f(A), then there exists a number μ € [m, M] such that S₁ 19 fg = μ 9.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Prove the following statement.

 

(b) Let A € D(R²) and
m = = inf f(A) and M
suppose ƒ and g are integrable on A. Let g(x) ≥ 0 for all x € A. If
sup ƒ(A), then there exists a number µ € [m, M] such that
=
Lo
S
fg= μ
9.
Transcribed Image Text:(b) Let A € D(R²) and m = = inf f(A) and M suppose ƒ and g are integrable on A. Let g(x) ≥ 0 for all x € A. If sup ƒ(A), then there exists a number µ € [m, M] such that = Lo S fg= μ 9.
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