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WTW258: LU 2.1: DOUBLE INTEGRALS AND ITERATED INTEGRALS Lecture notes $4.74   Add to cart

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WTW258: LU 2.1: DOUBLE INTEGRALS AND ITERATED INTEGRALS Lecture notes

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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

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  • July 13, 2022
  • 9
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes
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2. 1 .
Double integrals i


iterated integrals
Revision :
Riemann sum
Riemann sum
f- (a) Ca , b)
-




y
-




, Area =
f- ( ti ) ✗ DX
,

""
f- ( 1- 2) Dkz



;
^ Area
=

,




Area =
fits )n↳
-
5 > Approximation
t2 1- 3
~
dt ,

b

→ 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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