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

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SUMMARY

The discussion centers on solving a line integral defined by the equation ∫_C ((y-z)dx + (z-x)dy + (x-y)dz) over the curve C, constrained by the equations x² + y² + z² = 1 and y = √3x. The user suggests making the substitution y = √3x, which simplifies the curve to 4x² + z² = 1. The integrand is then transformed to ((√3 - 1)∫_C zdx - xdz). The application of Green's Theorem is recommended as a method to evaluate the integral.

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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
 
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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.
 
Thank you so much

i will try to work from there :)
 

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