Question

help with this super long integration!!
stokes theorem

Answer 1

help mee get this some how i tried using divergence theorem too the integral still looks ugly

Answer 2

can you input this integral in some program you can use, i tried wolfram. too big for it, or the computation takes too long it wants me to pay up

Answer 3

curl \(\overrightarrow{F}\) = \(<-3xyz^2, -2xz^4 + x + 2yz, yz^3 - z^2>\)
and since your surface, Since S is a closed surface, that means divergence thrm.
\(\int \int s~curl\overrightarrow{F}\cdot dS\)
\(\int \int s~<-3xyz^2, -2xz^4 + x + 2yz, yz^3 - z^2> dS\)
\(\int \int \int div~<-3xyz^2, -2xz^4 + x + 2yz, yz^3 - z^2> dV\)essentually, equal 0

and by the (div(\(curl~ \overrightarrow{F})\)= 0 identidy, you dont need to go further

Answer 4

what are you doing xD

Answer 5

but this isnt div X curl F you either do the stokes
by double int curl F . n ds
or triple intdiv F dv

Answer 6

both of which are just not simplifying for me, or maybe im just failing to see a nice way to simplify

Answer 7

i used divergence theorem triple integral.

Answer 8

okayy soo how u get 0 lol

Answer 9

u cant do div curl F
u gotta just do div F dv

Answer 10

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

Answer 11

yess i know this stuff

Answer 12

im not having trouble with concept just the integration is a b***CH

Answer 13

dbl integral (6sinxcosy) (6sinxsiny) (6cosx+1)^2, (6sinxcosy)+2 (6sinxsiny) (6cosx+1)-2 (6sinxcosy) (6cosx+1)^4, -7-(6cosx+1)^2+(6sinxsiny) (6cosx+1)^3} dot (36*sin^2xcosy,36sin^2xsiny,-72sinxcosx)
this for dxdy over 0<x<pi/2, 0<y<2pi

Answer 14

i used MATLAB.

Answer 15

i got this for the top half of the hemisphere

Answer 16

since it closed surface. u can use div thm

Answer 17

i know the divergence theorm has these sin^2 xs i dunno how to simplify it

Answer 18

\(\int \int \int [-3yz^2 + 2z + (3yz^2 - 2z)] dV\)

Answer 19

I did not parametrize if that is what you're doing.

Answer 20

where are you getting that formula from this is divergence isnt it