Question

Use Stokes' Theorem to calculate the circulation of the field F around the curve C when F and C are the following:

F= (x^2)i+(2x)j+(z^2)k
C= 4x^2+y^2=4 in the xy-plane

Answer 1

find curl of F= (x^2)i+(2x)j+(z^2)k

Answer 2

And how do I do that?

Answer 3

http://upload.wikimedia.org/wikipedia/en/math/8/e/8/8e818d1115abc22b39e736e9c704ed93.png

Answer 4

So i take the cross product of the individual components of the vector and the partial derivatives to find the curl. That I get. Where do I go from there?

Answer 5

get a surface , any surface whose boundary curve is C

Answer 6

So C is given by the problem. Then what?

Answer 7

you have to find a surface (an easy one) whose boundary curve is C

Answer 8

4x^2+y^2=4 is a ellipse

Answer 9

follow this
http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx

Answer 10

So I need to parametrize C first...but I'm not really sure how to do that.

Answer 11

is it [r=4\cos \theta I + \sin \theta J + K\]

Answer 12

r=4cos(0)i + sin(0)j + k where 0 = theta

Answer 13

hold on, let me think it through

Answer 14

r=cos(t)i+2sin(t)j+k
F(r(t))=cos^2(t)i+2cos(t)j+k
dr/dt=-sin(t)i+2cos(t)j
F(r(t)).(dr/dt)=-sin(t)cos^2(t)+4cos^2(t)
integration from 0 to 2pi of this gives 4pi