How do I solve this line integral problem with given constraints?

[nizama]

Hi!

I had exam today and i got one task that i am not sure how i should have made it so i hope you can help me with this one

It goes :

Find the line integral (i'm not good with using symbols so i'll do my best here)
integral by line C from (y-z)dx+(z-x)dy+(x-y)dz
int_C ( (y-z)dx+(z-x)dy+(x-y)dz )
and C is given by
(x^2)+(y^2)+(z^2)=1
y=x(sqrt3)

thanx a lot in advance and hope to hear from any of you soon

 

[quantumdude]

If you make the substitution y=(3)^1/2x, then you get for C:

4x²+z²=1

and you get for your integrand:

((3)^1/2-1)∫_Czdx-xdz

I'd use Green's theorem from there.

 

[nizama]

Thank you so much

i will try to work from there :)