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2D integral

  1. Apr 15, 2006 #1
    Problem:

    "Draw a Diagram to show over which area the following integral (see integral in attached file) is integrated."

    I drew a little diagram of what I think the area looks like (see diagram). But I am very, very insecure about what I did and would appreciate if anyone could have a look at it and let me know if I did something wrong. That would be really helpful!
     

    Attached Files:

  2. jcsd
  3. Apr 15, 2006 #2

    TD

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    Homework Helper

    I can't see the attachments yet, perhaps you could give the integral and the area? Try LaTeX :wink:
     
  4. Apr 15, 2006 #3
    [tex] \int {2x^2+y} dxdy [/tex]

    and the boundary conditions are

    for x: y < x < 2-y

    for y: 0 < y < 1

    hope that helps
     
  5. Apr 15, 2006 #4

    HallsofIvy

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    The outer integral is y so first draw to horizontal lines at y= 0 and y= 1 to define the limits for y. Now, for each y, x lies between y= x and x= 2- y which is the same as y= 2- x. However, in your picture you have x running between 0 and x. Move your stripes (indicating the figure) to the triangle formed by y= x, y= 2- x, and y= 0. (0f course, you notice that y= 2- x and y= x cross at y= 1.)
     
  6. Apr 16, 2006 #5
    thanks for this!

    I'm not sure whether this second attempt is right, but here is the new diagram anyway (with inverted strips):
     

    Attached Files:

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