Doubter Integrals
For fcx y )
, ,
the volume under the surface ,
the R
over
region ,
is
given by :
V =
SIR f- cosy ) d. A
No
integration techniques
>
new
'
>
Getting R' is hardest part of double integrals
, Fubini 's Theo rum
DA =
Ax .
Ay
Ay DX
=
.
dx
dy
=
.
dy dx
=
.
For
rectangular regions : 2 :{ cosy a ex ← b
;
c =
y
ed }
Y
#
d
the volume
÷
c
under this rectangle
✗
b
: 2
ways
to setup any double integral
IS fcx y ) doody , or IS fcx g) dy
,
-
doo
Y X X Y .
>
Make sure order of bounds
3
dy.dk Match
✓
Set whatever
in
up
easiest to solve
way is
integrals
For fcx y )
, ,
the volume under the surface ,
the R
over
region ,
is
given by :
V =
SIR f- cosy ) d. A
No
integration techniques
>
new
'
>
Getting R' is hardest part of double integrals
, Fubini 's Theo rum
DA =
Ax .
Ay
Ay DX
=
.
dx
dy
=
.
dy dx
=
.
For
rectangular regions : 2 :{ cosy a ex ← b
;
c =
y
ed }
Y
#
d
the volume
÷
c
under this rectangle
✗
b
: 2
ways
to setup any double integral
IS fcx y ) doody , or IS fcx g) dy
,
-
doo
Y X X Y .
>
Make sure order of bounds
3
dy.dk Match
✓
Set whatever
in
up
easiest to solve
way is
integrals
