Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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22.G

22.G. Let g be monotone increasing on J (that is, if x < x', then g (x) < g(x')).
Show that f is integrable with respect to g if and only if for each e > 0 there is a
partition P. of J and that if P = (xo, x1, ...,
; and n; belong to [r;-1, x;), then
Xn) is a refinement of P. and if
%3D
E \f(E;) – f(n1)|lg (x;) - g(Tj-1)} < e.
j=1
Transcribed Image Text:22.G. Let g be monotone increasing on J (that is, if x < x', then g (x) < g(x')). Show that f is integrable with respect to g if and only if for each e > 0 there is a partition P. of J and that if P = (xo, x1, ..., ; and n; belong to [r;-1, x;), then Xn) is a refinement of P. and if %3D E \f(E;) – f(n1)|lg (x;) - g(Tj-1)} < e. j=1
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