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Where to start?

  1. Nov 28, 2007 #1
    Okay I have no idea where to start on this example problem:

    Use polar coordinates to evaulate the double integral e^((x^2)+(y^2))dydx
    [frist (inner) integal lower limit y= -sqrt(4-x^2) upper limit y=0)]
    [second (outer) lower limit x=0 upper limit x=2]

    When I start doing the integral of e^((x^2)+(y^2))dy I get some really crazy answer and then I dont know if I should put it in polar coordinates before I try and take the integral or after. Can you tell me where to start?
     
  2. jcsd
  3. Nov 28, 2007 #2

    HallsofIvy

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    How in the world would you get "some really crazy answer"? It's pretty well known that there is no elementary anti-derivative for [itex]e^{-x^2}[/itex]- not even a "crazy" one!

    Also, since the problem is to evaluate the integral, I would see no point in changing to polar coordinates after integrating!

    What do you start? By doing what the problem says: "use polar coordinates"!
    Of course [itex]e^{-(x^2+ y^2)}[/itex] converts to [itex]e^{-r^2}[/itex]. Do you know how dydx converts?

    To get the limits of integration, draw a picture. [itex]y= -\sqrt{4- x^2}[/itex] is the lower half of the circle [itex]x^2+ y^2= 4[/itex] which has center at the origin and radius 2. x going from 0 to 2 means you are to the right of the y-axis. The region you are integrating over is the lower right quarter of a circle of radius 2. How do r and [itex]\theta[/itex] change to cover that region?
     
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