4.2 The De nik Integral
Oct: The de nite integral of f
b]
over [ų, 6] is the vet signell
yw y = f(x) and the c-axis a boy ha, 6] and is devoted by
b
5fcx)dx
and bare the love and
.
• f(x) is
the integrand
upper
limits of integration
• dx tells us the variable of integration
•If so far de exists, we say f is integrable
ху
Fucks: 1. it f is continuous on (a,b)
a
nite sex of.
is integrable on (a,b)
nimp
aver
[a,b]
or is continuous except for
dis continuities on [a,b] then f
2 { "Roxy dx = lim ng ? fex;) ox where x; = uti Ax and
Cxample: (lost tine)
=
example:
S² 2x²= xdx
6-9
Ax =
h
Evaluate this by taking the limit of a Riemann sun
Acx)=2x²-x = x(2x-1)
•
Ax=
x= b-a 20-2
:
^
Ax
X; = a+ : Ox
=0+ (2)
2
R = {fcx;)ox=
BX
{(4)
n 131
=
Zi
n
ичл
fi fifi
Oct: The de nite integral of f
b]
over [ų, 6] is the vet signell
yw y = f(x) and the c-axis a boy ha, 6] and is devoted by
b
5fcx)dx
and bare the love and
.
• f(x) is
the integrand
upper
limits of integration
• dx tells us the variable of integration
•If so far de exists, we say f is integrable
ху
Fucks: 1. it f is continuous on (a,b)
a
nite sex of.
is integrable on (a,b)
nimp
aver
[a,b]
or is continuous except for
dis continuities on [a,b] then f
2 { "Roxy dx = lim ng ? fex;) ox where x; = uti Ax and
Cxample: (lost tine)
=
example:
S² 2x²= xdx
6-9
Ax =
h
Evaluate this by taking the limit of a Riemann sun
Acx)=2x²-x = x(2x-1)
•
Ax=
x= b-a 20-2
:
^
Ax
X; = a+ : Ox
=0+ (2)
2
R = {fcx;)ox=
BX
{(4)
n 131
=
Zi
n
ичл
fi fifi
