Let C be the semi circle on the surface $\displaystyle x^2+y^2+z^2=4$ from $\displaystyle N=(0,0,2) $to $\displaystyle S=(0,0,-2)$ which passes through the point ($\displaystyle \sqrt{2}$,$\displaystyle \sqrt{2}$,$\displaystyle 0$) (note that x=y for all (x,y,z) on C.)

Evaluate the integral

$\displaystyle \int _c\!z^2dx + 2x^2dy + xydz$

(Suggestion: use as your parameter the angle Q subtended at the orgin by the arc NP for a point P on C)

I think i need to sketch the picture to understand it, but Im having a hard time to do it, is there another way to find x,y,z in term of t?