- #1
coljnr9
- 5
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Homework Statement
Let [itex]\vec{F}=<xy,5z,4y>[/itex]
Use Stokes' Theorem to evaluate [tex]\int_c\vec{F}\cdot d\vec{r}[/tex]
where [itex]C[/itex] is the curve of intersection of the parabolic cylinder [itex]z=y^2-x[/itex] and the circular cylinder [itex]x^2+y^2=36[/itex]
Homework Equations
Stokes' Theorem, which says that [tex]\int_c\vec{F}\cdot d\vec{r}=\int\int_s ∇×\vec{F}\cdot d\vec{S}[/tex]
The Attempt at a Solution
Because we are in the chapter of Stokes' Theroem, I am supposed to integrate over a surface that is defined by the intersection of the two surfaces given in the problem. However, I am having a bear of a time coming up with what that surface would look like, and what an equation for it would be.
I tried plugging the equations into a LiveMath module to see the intersection, but it would break as soon as I zoomed out far enough to see what I needed.
When I have to do this with other problems (intersection of a parabloid and a cylinder), I can look at the graph, or just imagine it, and fairly quickly see the general shape, and then do some algebra to get the coefficients.
If I could have some help coming up with the equation of that surface, I would be able to do some dot-and-cross products and be on my merry way.
Thanks!