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Choosing the order of integration with double integration

  1. Jan 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Sketch the regions of integration, and evaluate the integral by choosing the best order of integration.
    [tex]\int^{2\sqrt{ln2}}_{0}\int^{\sqrt{ln2}}_{y/2}exp(x^2)dxdy[/tex]


    2. Relevant equations
    integration by parts


    3. The attempt at a solution
    ive changed the order of integration and done the inner integral with respect to y to get this far..
    [tex]\int^{\sqrt{ln2}}_{y/2}\int^{2\sqrt{ln2}}_{0}exp(x^2)dydx=\sqrt{ln2}\int^{2\sqrt{ln2}}_{y/2}exp(x^2)dx[/tex]

    and now when i do a u substitution
    [tex]u=x^2[/tex]
    [tex]du=2xdx[/tex]
    and that is how far i can get as i can't put the 'du' into the equation as it has a '2x' in it and i will be integrating with respect to 'u'. Integrating it the original way round just gets me to this problem straight away.

    I just can't see any way of getting rid of the 2x?!
     
  2. jcsd
  3. Jan 6, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    If you change the order by which you integrate, the limits will change. You need to find the new limits.

    Also ∫ex2dx does not exist in terms of elementary functions.
     
  4. Jan 6, 2010 #3

    Mark44

    Staff: Mentor

    Make sure you sketch the region of integration, as step that many students skip, believing it to be unimportant.
     
  5. Jan 6, 2010 #4
    that seems so obvious now but you wouldn't believe how long ive been looking at it, the 'cancelling 2x' comes from when you change the limits. thanks guys!
     
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