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Xy coordinates to polar coordinates for double integral. hepl please!

  1. Jan 31, 2009 #1
    1. The problem statement, all variables and given/known data
    ok change the region R = { (x,y) | 1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA


    2. Relevant equations
    r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@)


    3. The attempt at a solution

    i got R = { (rcos(@), rsin(@) | 1 <= r <= 2 , 0 <= @ <= pi/4 }

    and 3/8 * pi ^2 answer in back of book is 3/64 * pi ^2


    thankyou for your time!
     
  2. jcsd
  3. Jan 31, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    You've correctly converted to polar coordinates and found the limits of integration, but you somehow made a mistake evaluating the integral...Did you by chance forget that you are integrating the function [itex]\tan^{-1}\left(\frac{y}{x}\right)=\theta[/itex] over this region, andf just find the area of the region instead?:wink:
     
  4. Jan 31, 2009 #3
    thankyou veeery much!
     
  5. Jan 31, 2009 #4

    Mark44

    Staff: Mentor

    Not sure this made a difference in your answer, but the equations for x and y above are wrong. They should be
    x = r*cos(theta)
    y = r*sin(theta)
     
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