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WTW256: LU 2.2: DOUBLE INTEGRALS IN POLAR COORDINATES Lecture notes $4.72   Add to cart
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WTW256: LU 2.2: DOUBLE INTEGRALS IN POLAR COORDINATES Lecture notes
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  • Course
  • WTW 258 - Calculus
  • Institution
  • University Of Pretoria (UP)

Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover Double integrals in Polar coordinates.

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Document information

  • July 13, 2022
  • 8
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

Subjects

  • wtw
  • 258
  • wtw258
  • calculus
  • double integrals
  • polar coordinates
  • density
  • mass

Written for

  • University of Pretoria (UP)
  • WTW 258 - Calculus
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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

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