Question

stokes theorem

Answer 1

http://gyazo.com/ad63f389a32cda1ecf9e79c11acc8eaf

Answer 2

im not sure how to parametrise this

Answer 3

the curve of intersection or the plane to do stokes?

Answer 4

plane:
R(x,y)=<x,y,y+1>
Curve of intersection:
R(t)=<cos t,sint,sint+1>

Answer 5

do not try to intergrate over the curve it will get ugly

Answer 6

stokes simplies a lot
so do integral <Del X F> .<Rx X Ry> dxdy
over the domain x^2+y^2=1

Answer 7

do it in polar

Answer 8

i have to find the normal vector first right?

Answer 9

Rx X Ry gives u normal vector

Answer 10

the parametrisation is ( rcos(theta) , rsin(theta) , sin (theta) +1 ) , right?

Answer 11

thats the paretrization of the curve

Answer 12

you wanna use the plane

Answer 13

do i differentaite partially r(x,y) to find the normal vector?

Answer 14

diff R wrt to X and R with y and cross them both

Answer 15

The cross product of 2 independent vectors of a plane will give you a normal vector to that plane

Answer 16

ok i got ( 0, -2x+4,-2) . (1,-1,1)

Answer 17

do i use polar coordinates for this?

Answer 18

u can use dxdy too try to see what happens then

Answer 19

also dont think the normal vector you calculate is right

Answer 20

(1,-1,1) for normal vector

Answer 21

(0, -2x +4 , -2) for curl

Answer 22

the normal vector should have no component in the x direction

Answer 23

yeah (1,-1,1) is what i got for the normal vector

Answer 24

its wrong

Answer 25

(0,1,1)

Answer 26

wait (0,-1,1)

Answer 27

yes carry on

Answer 28

you should watch these video ocw MIT multivariable calculus

Answer 29

theyre very nice, and easy to undertand

Answer 30

it will clear up all confusion

Answer 31

i must go to bed now

Answer 32

okie thanks