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Homework Help: 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


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    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
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