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!

Vector Calculus: Surfave Integrals

  1. Apr 16, 2009 #1
    Vector Calculus: Surface Integrals

    1. The problem statement, all variables and given/known data
    Find the surface integral of u[/B dot n over S where S is part of the surface z = x + y^2 with z < 0 and x > -1, u is the vector field u = (2y,x -1,0) and n has a negative z component


    2. Relevant equations



    3. The attempt at a solution
    How do you "find" the surface. I have just started ont the subject and I have no idea how to see what is the surface and the region of integration.

    Solution according to the book
    The surface is written parametically as (x,y,x+y^2)
    two vectors parallel to the surface are (1,0,1) and (0,1,2y)
    Their cross product = (-1,-2y,1)
    ndS = (-1,-2y,1)dxdy
    changing the direction of n
    ndS = (1,2y,-1)dxdy
    u dot ndS = xdxdy
    region of integration x+y^2 < 0, x > -1, so doing the x integration first, -1<x<-y^2 and
    -1 <y <1
     
    Last edited: Apr 16, 2009
  2. jcsd
  3. Apr 17, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    hey MaxManus

    to visualise the surface, consider the curves given by y = 0 and x = 0, ie the surface slices by the xz & yz planes, this should be a good starting point
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Vector Calculus: Surfave Integrals
Loading...