November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
Content preview from Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
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D.6 INTEGRAL FORMULAS
For convenience, we provide expressions for Leibniz's integral rule:
(D.71) 
and for integration by parts:
which is written using Riemann–Stieltjes integrals. If the functions are differentiable everywhere on [x1, x2], then 
and 
, yielding
(D.73) 
For an indefinite integral and suppressing the variable x, (D.72) can be written as
(D.74) 
which is the familiar form covered in calculus courses.
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