WTW258: LU 2.1: DOUBLE INTEGRALS AND ITERATED INTEGRALS 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 and iterated integrals
→ Divide interval into smaller intervals
[ intervals don't have to be same
length )
→ Area btw .
f and a- d ✗ is 0h [9lb ]
≈ § f- ( th ) Dan .
§ Jab f- (x ) da k -1
-
Now consider d function of 2 Variables defined on a
rectangle R
→ Divide R into smaller rectangles
→ choose a point in
every small rectangle Caij yij ) ,
→ volume of
small
=
flxij yij ) ,
Dui DYI
black
Riemann sum =
Double integral
?⃝
, tim
miso
h→o
↑ I flxij
it j=1
, yij ) ☐A
} Riemann
sum
JJ fix ,y)dA
⑥ A)
R
→ if f- (a) y ) ≥ 0 the volume of the solid above R
,
region
below the function 2- = fl≥ ,y ) is :
Sf fix,y)dA
r ¥ .
HOW DO WE CALCULATE SS tiny)dA ?
R
'
① Describe region retype
type 2 region
① writedbitgrdasiterdtedintegrals
TYPE I l vertical )
A region Rin R2 is a type 1 region it
R= { cxiy ) / a ≤
✗ ≤ b
g.cn,
≤ y ≤ gzcx ) }
,
Lcenstdhts
a- 9164
•
btw
bg
" •
btw 2 functions
• >
•
btw2-r-ieli.net
, ,≥,
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