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Homework Help: How to evaluate this double integral?

  1. Dec 19, 2011 #1
    1. The problem statement, all variables and given/known data

    ∫0 to 2 ∫x/4 to 1/2 (sin (pi*y2)) dy dx

    2. Relevant equations

    3. The attempt at a solution

    I think I have to convert this to polar or do some sort of change of variable.

    Although in polar y = r sin θ, so then you would have sin of a sin??
  2. jcsd
  3. Dec 19, 2011 #2
    Try drawing the region and switching the order of integration, and this might allow you to use substitution rule hopefully, as I believe you will get something of the form [itex] \int y*\sin(\pi y^2) dy [/itex]
  4. Dec 19, 2011 #3


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    Sketch the region (in the xy-plane) over which the integration is being done. Use this to switch the order of integration.
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