contour integral...

could someone please verify that my answer is correct to this as i`m not sure:

Evaluate $\int_{C} dz$

where C: $\displaystyle \frac{x^{2}}{36}+\frac{y^{2}}{4}=1$

from $z=2i$ to $z=-2i$

my solution:

parametrized z curve: $z(t)=6 \cos(t)+2 \sin(t)i$

so

my answer is $\displaystyle -4$

am i correct? or would i get a different answer (the correct one) by splitting the left part of the ellispe into an upper then lower curve, and integrating along each successive curve?

What's happened to the 'i' in your dz?

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Your answer is wrong. If you correct for not having the 'i' in dz, you should get the right answer, but from your previous post I'm not sure if you did have the 'i' in dz, you just didn't put it in the post. (In which case you will need to post your working - as your current answer is wrong).

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So, now that you've got the right answer, note that if this was a "normal" (not complex) integral, you'd go:

$\displaystyle \int_a^b \, dz = [z]_a^b = b - a$, where a, b are your start/end points, respectively.