Integral Calculus Office Hour 1 Notes
t
tigjfnq.tw xandy fabflxmldx
2 Iterative integral fdfabflg.gg fed fabfix y dx dy
3 Theorem on order fedfab fabled
Example Jj f x y dxdy
first evaluate inside fix'ty dx 3 3
42 7É342 3dy
thencalculatetheoutside II
Example If ypdydx firstinside f pdx Ey
then calculate outside giving fi Iata dx
this
Example
Ifusing ysinx first integrate xsing ysinx
x'singtycost
then outside
fi tf y III Asifa y
Example
23715rad
24 SÉydx 3 37,4 343 33.13Fate
25715nF
a TMI
Douby.gg1Yffn YffeIgttain tunes g audg such that
R a exe b g Cx EYE 92 x
this means
LISLE
If fix g dA fabfog fix g dydx
whentimitisinsfunction alwaysinside
douban.ggerguingsTjhhttitsy axis like this
It
a x2 X Fx x 1
Type I I f fly g dxdy interior limitsalongy
Typez L Ii tuna ax
ÉfÉ Si SIIfixiddxdx
siteType2 Si f.fi flxiy
dxdyEgYfTdAR 14 2 osx's
S S xy2dxdx f Ey 124
is 81274 8 8
MIMI So fly'xdydx t fi fi yaxdied
d
Sos exterior
interior Y dydx 1 7725ydydx
g EST
y X 5