- #1

- 255

- 0

[tex] \int_{D} f_{y}(x, y, z)dxdydz = \int_{\partial D} f(x, y, z)n_2(x, y, z)dS[/tex]

I think I see how they might be equal but I don't know where to start as far as proving it.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Tony11235
- Start date

- #1

- 255

- 0

[tex] \int_{D} f_{y}(x, y, z)dxdydz = \int_{\partial D} f(x, y, z)n_2(x, y, z)dS[/tex]

I think I see how they might be equal but I don't know where to start as far as proving it.

- #2

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 10,025

- 134

Hint:

Consider the vector function:

[tex]F(x,y,z)=(0,f(x,y,z),0)[/tex]

Consider the vector function:

[tex]F(x,y,z)=(0,f(x,y,z),0)[/tex]

- #3

- 255

- 0

While we're on it, I have another similar question. Say F:R^3 -> R^3 is a C^1 function, verifty that

[tex]\int_{\partial D} \nabla \times F \cdot n dS = 0 [/tex]

in two ways, first using Stokes theorem, then using the Divergence theorem.

By the way, I'm currently in vector calculus and at the same time first semester PDE. We don't cover the divergence theorem and such until way later into the semester. But our PDE book requires that you have some minor knowlegde of these theorems. And thats what our professor is having us do right now, especially for those of us that are currently in vector calculus.

[tex]\int_{\partial D} \nabla \times F \cdot n dS = 0 [/tex]

in two ways, first using Stokes theorem, then using the Divergence theorem.

By the way, I'm currently in vector calculus and at the same time first semester PDE. We don't cover the divergence theorem and such until way later into the semester. But our PDE book requires that you have some minor knowlegde of these theorems. And thats what our professor is having us do right now, especially for those of us that are currently in vector calculus.

Last edited:

Share: