МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
ТЕОРИЯ И ПРАКТИКА
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Clearly and not clear of integrals economic in processes application
Jumayeva Shahnoza Farhod qizi
Asia International University , " General Engineer". Department of Sciences
teacher
shahnozafarhodovna79@gmail.com
Abstract.
This in the article sure and not clear of integrals in the economy
applications analysis will be done . Economical processes in modeling and in
assessment from integrals how use possibility , especially the income optimization ,
costs management , consumer and work issuer surplus such as economic issues in
solving application seeing will be released .
Key words
: definite integral, indefinite integral, economic modeling ,
consumer surplus , production issuer surplus , capital accumulation , demand and
offer
Enter
In economics mathematician methods apply not only theoretically , maybe
practical is also important is considered Growth pace assessment , income and
expenses analysis make , the optimal investment and work release strategies in
choosing sure and not clear integrals main from tools is one . These are methods
economic of processes time according to how change , demand and offer between
relationship to understand for is used . Especially the macro and microeconomic
analysis mathematician respectively in expression they are big importance
occupation is enough
Clearly integrals known boundaries between economic of processes common
size or value in the calculation is used . For example , general income , consumers
and work of producers surpluses in determining is used .
МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
ТЕОРИЯ И ПРАКТИКА
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Uncertain integrals while given economic of processes common expression to
find help gives They are using of change how at pace happened to be and capital or
another economic of indicators how get together to go to determine can Clearly and
not clear integrals in economics many issues in solving use can , for example , capital
accumulation , economical growth pace calculation , profit and expenses
optimization such as . This this is the article issues mathematician analysis using
seeing comes out and sure examples based on their in the economy role shows .
Precise integral function under the field count through meeting process
represents Mathematics and economic in the models this field most of the time
amounts , profits or expenses with depend
( )
( )
( )
b
a
f x dx
F b
F a
,
this on the ground
( )
f x
function and
[ , ]
a b
between field is (Chart 1).
Drawing 1
Precise integral economic functions known one in between common size to
count service does This method the following processes for applies to :
1. General income calculation
: Income function to time tied up using the
definite integral common income to determine For example ,
( )
R t
income function
known time between
1
t
from
2
t
to if , general income to find for the following definite
integral is used :
МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
ТЕОРИЯ И ПРАКТИКА
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2
1
( ) .
t
t
Umumiy daromad
R t dt
An example for , enterprise by work issued of products income count for time
in the interval
0.05
( ) 1000
t
R t
e
function given in between integration as a result
common income
10
0.05
0
1000
t
e
dt
is considered This while enterprise o ' shine analysis
to do help gives
2. Iste ' molchi and work issuer surplus
: Demand and offer curve lines
between the field sure integral using count Consumer surplus to find for demand and
price curve lines between the field to find need : Consumer surplus
0
'
( )
( )
,
P
d
s
Iste molchi profitsiti
Q P
Q P dP
Here
( )
d
Q P
demand function ,
( )
s
Q P
while offer is a function of .
For example , if the demand function
200 5
d
Q
P
, offer function while
50 3
s
Q
P
if , using the definite integral consumer of the surplus common volume
as follows is :
2
2
0
0
'
200
5
200
2.5
200
2.5
P
P
Iste molchi profitsiti
P dP
P
P
P
P
Indefinite integral economic variables in finding wide is used . The following
practical manuals this shows :
1. Capital accumulation
: Capital time according to to change expressive
growth model in creating indefinite integral is used . If capital change pace equation
through given if ,
dK
rK
dt
, then this of Eq not clear integral the following in
appearance will be :
0
( )
.
rt
K t
K e
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Through this formula of capital time according to how growth observation can
Capital Accumulate in the model time according to growth pace was determined .
2.
Demand and offer functions again recovery
: If economic of the process
derivatives given if , using the indefinite integral this of the function common
appearance recovery can For example , the demand function grow pace
5
d
dQ
P
dP
if
, using the integral recovery can :
2
( )
5
2.5
,
d
Q P
PdP
P
C
Here
C
is the demand function initial value determiner permanent
Conclusion .
Clearly and not clear integrals in economics important analysis of means one
they are different economic processes in modeling efficient is used . Clearly integrals
using common income , expenses and benefit such as indicators count can These are
the indicators enterprises and economic of systems financial the situation sure
analysis to do and manage for important Consumer and work issuer surpluses to
determine while demand and offer functions based on economic processes deeper to
understand help gives Uncertain integrals using economic of processes time
according to to change analysis to do opportunity appear will be For example ,
capital tumor modeling of enterprises future financial situation prophecy in doing is
used . This methods economic decisions acceptance making investments in planning
and economic politics in formation important role plays This of integrals main
advantages economic processes more precisely assessment , time pass with changes
modeling and economic of systems efficiency to increase directed . In the future
more complicated economic models analysis to do for of integrals application field
expand and mathematician methods development necessary Integrals economic
МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ:
ТЕОРИЯ И ПРАКТИКА
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processes deeper analysis to do and efficient manage for main from tools one as
service does
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