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Math Help - Polar Coor Intergration Help

  1. #1
    Junior Member
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    May 2009
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    Polar Coor Intergration Help

    i need help on the follow problem

    Ive tried this several time, and cant tell if my bounds are incorrect or if something else im doing is incorrect. I really need some help, my tutor couldn't do it either n shes better at math then i am.
    Integrate f (x,y) over D using polar coordinates.
    Attached Thumbnails Attached Thumbnails Polar Coor Intergration Help-symimage.cgi.gif   Polar Coor Intergration Help-symimage-1.cgi.gif  
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  2. #2
    Super Member
    Joined
    Aug 2008
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    So you're integrating over the blue region in the plot below right? Then doesn't that red line go from \pi/4 to 3\pi/4? Then the radius will go from where the red line intersects the line at y=1/\sqrt{2} to one right? That's at the blue point. Can you show how the radius at the blue point is r=\frac{csc(t)}{\sqrt{2}}? Then the integral is:

    \int_{\pi/4}^{3\pi/4} \int_{\frac{\csc(t)}{\sqrt{2}}}^1 \frac{sin(t)}{r^4} dr dt

    Looks to me anyway. Go over it and double check everything.
    Attached Thumbnails Attached Thumbnails Polar Coor Intergration Help-circleplot.jpg  
    Last edited by shawsend; November 10th 2009 at 04:44 PM. Reason: corrected formula
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  3. #3
    Junior Member
    Joined
    May 2009
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    you are correct sir

    i actually figured it out little while ago, thanks for the help anyway

    idk what i was doing wrong, i let maple do the work for me =-)
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