12.2 The Definite Integrals (5.2) - University of Utah
[Pages:6]Course: Accelerated Engineering Calculus I Instructor: Michael Medvinsky
12.2 The Definite Integrals (5.2)
Def: Let f(x) be defined on interval [a,b]. Divide [a,b] into n subintervals of equal
width
x =
b-a n
,
so
x0
= a, x1 = a + x, x j
=a+
jx, xn
=b.
Let
x*j
be
an
arbitrary
(sample)
points such that x*j ( ) xj-1, xj . Then the definite integral of f from a to b is
b
n
f
(x)dx = lim f n
( )x*j x
provided
that
the
limit
exists.
If
it
douse
exist,
we
say
that
f
is
a
j=1
integrable on [a,b].
Notes:
? is an integral sign, f(x) is an integrand and a, b are lower and upper limits
of the integral respectively. Evaluating\calculating the integral is called
integration.
b
b
b
? The integral is not dependend on x, i.e. f (x)dx = f (t)dt = f (r)dr
a
a
a
? If f(x)>0 in [a,b], then an integral represent the area that lies under f(x). For
f(x) ................
................
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