Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

D.6 INTEGRAL FORMULAS

For convenience, we provide expressions for Leibniz's integral rule:

(D.71)

and for integration by parts:

(D.72)

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.