# Integrating over a closed contour following vector field

Integrate over a closed contour $c$ $$\oint_c d\vec{r}\times\vec{a}, \quad \vec{a}=-yz\vec{i}+xz\vec{j}+xy\vec{k}$$ where $c$ is cross-section of following two surfaces $$x^2+y^2+z^2=1$$ and $$y=x^2$$ oriented in a positive direction when looking from the positive direction of y axis.

That's the problem. Now, what have I done so far? I calculated $dr \times a$ and and used Stokes' theorem. Now I have a closed contour integral over ort $i$, $j$ and $k$. I can break it into 3 integrals, integral over $i$, $j$ and $k$. And that's where I'm stuck. What to do now?

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please avoid stating the questions as imperatives and try to show the steps you have taken towards the solution – Valentin Jun 5 '12 at 16:14
It's kind of a messy to post the question. I didn't finish with it. Wait for it. :) – Hasanaginica Jun 5 '12 at 16:15