1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Surface Integral

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Evaluate the surface integral [tex]\vec{F}\cdot\vec{n}\, dS[/tex]

    where [itex]\vec{F}=<-y,x,0>[/itex] and S is the part of the plane [itex]z=8x-4y-5[/itex] that lies below the triangle with vertices at (0,0,0,), (0,1,0,) and (1,0,0). The orientation of S is given by the upward normal vector. answer: 2

    I am not sure if I am just making a careless mistake or a conceptual one.

    3. The attempt at a solution

    i.) Parametrizing S gives [itex]\vec{r}(x,y)=<x, y, 8x-4y-5>[/itex]

    ii.) Finding [tex]\frac{\partial r}{\partial x}\times \frac{\partial r}{\partial y}=<1,0,8>\times<0,1,-4>=-8,4,1[/tex]

    iii.) Thus, [itex] \vec{F}(\vec{r}(x,y))\cdot (\frac{\partial r}{\partial x}\times \frac{\partial r}{\partial y})=<-y,x,0>\cdot<-8,4,1>=<4x+8y>[/itex]

    iv) Therefore [tex]I=\int\int_D (4x+8y)\, dA[/tex]

    [tex]=\int_{x=0}^1 \int_{y=0}^x (4x+8y)\,dy\, dx[/tex]

    I belive that if I made an error, it was made somewhere in here and not in my integration.

    Any major blunders here?

  2. jcsd
  3. Nov 30, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Look at your integral limits. You are integrating over the triangle formed by (0,0,0), (0,1,0) and (1,1,0).
  4. Nov 30, 2008 #3
    Not sure I follow. My x bounds are correct right?
  5. Nov 30, 2008 #4
    Is my upper y bound supposed to be (1-x)?
  6. Nov 30, 2008 #5


    User Avatar
    Science Advisor
    Homework Helper

    It sure is!!
  7. Nov 30, 2008 #6
    :redface: That's what I get for thinking I can do everything in my head...Teehee....
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Surface Integral
  1. Surface integral (Replies: 6)

  2. Surface integrals (Replies: 10)