Question

Surface Integral anyone?

Answer 1

no/.

Answer 2

no thanks .. not hungry :)

Answer 3

straight no.

Answer 4

{x^2 y, -x y^2, z}

over

x^2 + y^2 + z^2 =9

Answer 5

No divergence theorem

Answer 6

without Div theorem?
F * dS
dS=||Rx X Ry||
z^2+y^2+x^2=9
z=SQRT(9-(x^2+y^2))
(x,y,Sqrt(9-(x^2+y^2))
lets choose either spere or polar Theta=Q
R(r,Theta)=(rcos(Q),rsin(Q),Sqrt(9-r^2))
||Rr X RQ||=

i j k
cos(Q) sin(Q) -r/SQRT(9-r^2)
-rsin(Q) rcos(Q) 0
=r^2cos(Q)/SQRT(9-r^2)i+r^2sin(Q)/SQRT(9-r^2)+rk
TAKING THE MAGNITUDE=
HELP ME OUT IRANMEAH91

Answer 7

for some reason , it is only parameterize for sphere ; not other surface

Answer 8

did i not parameterize the surface correctly?

Answer 9

you did,but I am looking at examples and they only parametrize for sphere; not for paraboloid

Answer 10

whats the equation of a paraboliod
i could try to parameterize it

Answer 11

http://tutorial.math.lamar.edu/Classes/CalcIII/SurfIntVectorField.aspx

Answer 12

They just use the gradient for other surfaces

Answer 13

NO NO NO NO NEVER USE THAT S*** its the worst thing to use

Answer 14

ndS= do not every use delf/||delf||(delf))

Answer 15

lol, strong feeling

Answer 16

yes ok i think your speaking of n vector =delf/||delf|| right ?

Answer 17

yes

Answer 18

ok ill make it super easy for you
this may take a second

Answer 19

\[\nabla F/|\nabla F|\]

or

\[r_a \text{cross} r_b\] divided by it magnitude

Answer 20

if you have some function of x and y
like we did above
z=x+y
then f(x,y)=x +y
well when you parameterize the surface or whatever you do
its (x,y,f(x,y))
partial of z=f(x,y)=fx simular to fy
Rx X Ry=
i j k
1 0 fx
0 1 fy
Rx X Ry=(-fx,-fy,1)=ndS
so anytime you have to use ndS parameterize and shove it into the xy plane which you do by dotting it with ndS and integrate using brother greens method

Answer 21

so if your given z+y+x=1
z=-x-y+1
ndS=(1,1,1)

Answer 22

oh, I see; thankss

Answer 23

welcome and when you have
x^2/a^2+y^2/B^2=z
you can turn this into polar right now
(rcos(Q),rsin(Q),r^2cos^2(Q)/a^2+r^2sin^2(Q)/b^2)
then you ||Rr X RQ||drdQ=dS to do surface integrals though

ndS is for curl, div theroem