Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Some basic facts about integration. The case R2
 

Summary: Some basic facts about integration.
The case R2
.
Suppose R R2
. Then
(1)
R
f(x, y) dxdy =
R {y:(x,y)R}
f(x, y) dy dx
In particular, if f is the indicator function of R we find that
(2) Area(R) =
R
Length({y : (x, y) R}) dx.
An important special case is the following. Suppose - < a < b < ; , : (a, b) R;
(3) (x) < (x) whenever x (a, b);
and
R = {(x, y) R2
: x (a, b) and (x) < y < (x)}.
Then

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics