# Thread: Stoke's Theorem - Jacobian Problem

1. ## Stoke's Theorem - Jacobian Problem

Question asks to evaluate the surface integral for the given $\displaystyle F$ and $\displaystyle S$ with stokes theorem.

$\displaystyle F= [z^2, x^2, y^2], s: z^2 = x^2 + y^2$ for $\displaystyle y >= 0$, $\displaystyle 0<=z<=2$

My question is that in transformation from x,y to u,v shouldn't there be jacobian multiplied ? I dont see it anywhere in the solution.

2. Originally Posted by Altair
Question asks to evaluate the surface integral for the given $\displaystyle F$ and $\displaystyle S$ with stokes theorem.

$\displaystyle F= [z^2, x^2, y^2], s: z^2 = x^2 + y^2$ for $\displaystyle y >= 0$, $\displaystyle 0<=z<=2$

My question is that in transformation from x,y to u,v shouldn't there be jacobian multiplied ? I dont see it anywhere in the solution.
There is no trouble or mystery here.

The surface is being represented by the parametrised position vector $\displaystyle \vec{r}(u, v) = x(u, v) \vec{i} + y(u, v) \vec{j} + z(u, v) \vec{k}$. Using this representation, $\displaystyle \vec{dS} = \frac{\partial \vec{r}}{\partial u} du \times \frac{\partial \vec{r}}{\partial v} dv$.

This is a formula that should be somewhere in your notes or textbook.