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Is sketching the only way?

  1. Jun 27, 2004 #1
    If you want to find volume or area using double/triple integration, is graphing the (r) and (d) the only way to see if it is a type I, II, or III problem? I'm not really good at sketching planes so I'm having great difficulty finding the answer. But when it is already setup I can do it easily.
     
  2. jcsd
  3. Jun 27, 2004 #2
    What are type I, II, III? never heard of that before.
     
  4. Jun 27, 2004 #3
    They are just names for how we setup the limits of integration. A type one for double integration is when D={(x,y)| a<=x<=b, g1(x)<=y<=g2(x)}

    Type II is D={(x,y)| c <= x <= d, h1(y) <= x <= h2(y)}
     
  5. Jul 1, 2004 #4
    that depend upon how well u set up the problem, but skecthing helps
     
  6. Jul 18, 2004 #5
    Couldn't you choose? For example, for a double integral, where the region to integrate over is the triangle with vertices (0,0), (2,0), (0,1), the region could be set with:

    D = {x,y : 0 <= y <= -x/2 + 1 , 0 <= x <= 2} (type 1)

    or:

    D = {x,y : 0 <= x = 2y + 2 , 0 <= y <= 1} (type 2).

    But then of course to see the limiting function for either of these, sketching helps.
     
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