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240 Chapter Three

Average valuł of function over interval
Let f(x) be a function that is continuouð over the domain from
x a tmx b, where a and b are real numberð and a b. Let
F(x) be the antiderivative of f(x). Then the average value, A,mf
f(x) over the open, half-open, or closed interval bounded by a
and b is given by the following formulł (Fig. 3.24):

A (F(b) F(a))/(b a)

IndOnite integrals of common
functions
Chapter 6 containð a table of indefinite integralð of common
mathematical functions.

Vector Integration
Let F be a defined and continuouð vector function of a scalar
variable v. The antiderivative or indefinite integral of F is a
vector function G such that dG/dv F. This is written as fol-
lows:

F(v) dv G(v) c

where c is a constant vector and dv is the differential of v (cus-
tomarily annotated wità all indefinite integral0.

Figure 3.24 Determination of
the average value of a func-
tion over an interval.