WTW256: LU 2.2: DOUBLE INTEGRALS IN POLAR COORDINATES Lecture notes

2.2 .
Double integrals -

polar
coordinates
description of relevant surface
region R depends on

flu y ) ✗ 4- plane
① Describe Randy 2- i
i. to →
=
/
.




"

② f- 1747 ) ✗ 7- plane
"
11 and 2- → -


y y

"


① y and t YZ plane
"


fly ,z )
-



→ a. .




Polarcoordinatesrevision
Cr , A) → P.C.
Cosa
In
=




my
0
y)
X=r cos
• ( x/



g
To > a Sino =
Mr
v
y
-
-

rsino

Then ✗
21kg2 : r2

tano
=
Y /a

, Area of circle sector

Yzma


7h① Area of shaded part
DA



¥, Finna"
☐ A-

'
-
Yzripo
YZDACR
sector

-




' -
'
.




Yzrz Da

ri )
,


^
YZDO Cri rz )lr , )
-


=
-1h
o,
-

_




D8 ,
- -
=DODr(htarragon
'

,
' is
r ,
Dr ri
v




Theorem .




described it -0 polar coordinate,
If a
region R is .




a. ≤ o≤ Oz ,
g. (a)
≤ r ≤
goco)
with ◦ ≤ ( or
-




G) ≤ 21T then

f) fix ,y)dA
R