If $\vec{F} = 2y\hat{i} -z\hat{j} + x^2\hat{k}$ and $S$ is the surface of the parabolic cylinder $y^2 =4x$ in first octant bounded by planes $z =4$ and $z =6$ then
Evaluate $\displaystyle \int_{S} F.\hat{n}ds$
Now, My main issue is how can I decide the sign of Normal Vector $\hat{n}$. I am not able to see which direction is positive and which one is negative.
For $y^2 = 4x$ the Normal Unit Vector is given by :
$\hat{n}$ = $\dfrac{2\hat{i} - y\hat{j}}{\sqrt{y^2 + 4}}$. I am confused whether I should take
$\hat{n}$ or $-\hat{n}$ as the outward normal Unit Vector ?
Can someone help me here please ?
Thank you.