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WTW258: LU 2.3: TRIPLE INTEGRALS FOR FUNCTIONS OF THREE VARIABLES Lecture notes $4.60   Add to cart
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WTW258: LU 2.3: TRIPLE INTEGRALS FOR FUNCTIONS OF THREE VARIABLES 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 Triple integrals for functions of three variables.

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Document information

  • July 13, 2022
  • 9
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

Subjects

  • wtw
  • 258
  • wtw258
  • calculus
  • triple integrals
  • iterated integrals
  • volume
  • mass

Written for

  • University of Pretoria (UP)
  • WTW 258 - Calculus
All documents for this subject (24)

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functions with
2.3 .
Triple integrals 3 Variables

integrate over dsolid region c- in space 112¥:
Triple integrals
•
3 variable function
•

f) Jfk ,yidV
E ↓ ↳ volume
↓ new
Not that important
changed
.




Plane
name for Type 1,2 , } regions
-




C- projection .




region
inside → outside

Example
above the XY plane , below
① f is the region
-




'
the sphere ii. y *t
"
9 ? 3.
, exit
,
to ✗ Y Plane
project
-




✗
" enter
(7--0) '
9 a-
-



ji
prey
=


exit
V9 x2
⑧
'
≤ 2- ≤
◦
y
-
-




into
mentor
exits
cehtrdhle) µ

, •
≤ set }
Variable
-3
•
-

✓Ñ≤ y ≤ g- x2 function

volume of E
?

3 V9.7 ✓q-Ñ
JJJ
f
I dv
=L .
} f.gg#fo1dtdydk
First octant → where my ,t
positive
is



if we've got :




projected to
Type I
.
. .


dtdyd K ✗y
-


plane



Projected to Type 2

$ .
. .

dydxdz ✗ 7- plane
on

R outside .




to
Projected
$ . _ .
dxdydt YZ -



plane
Type 2

R




?⃝

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