Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) = 1 if x = [a, c] and F(x) = 0 if x € (c, b], the integral gdF exists and is equal to-g(c) Generalizes the above example to the case where F has n discontinuity points at [a, b].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following example: if g: [a, b] → R is continuous and F is a function defined
as F(x) = 1 if x = [a, c] and F(x) = 0 if x € (c, b], the integral gdF exists and is equal
to -g (c) Generalizes the above example to the case where F has n discontinuity points
at [a, b].
Transcribed Image Text:Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) = 1 if x = [a, c] and F(x) = 0 if x € (c, b], the integral gdF exists and is equal to -g (c) Generalizes the above example to the case where F has n discontinuity points at [a, b].
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