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Double Integral Problem!

  1. Jun 21, 2011 #1
    1. Find the area of the ellipse (2x + 5y − 3)^2 + (3x − 7y + 8)^2 < 1

    I have no idea what this looks like, and hence I cant figure out the limits. Maybe I could transform it into a more familiar form using a translation and rotation? Please help.
     
  2. jcsd
  3. Jun 21, 2011 #2

    Char. Limit

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    Have you learned about the Jacobian? This seems like a good place to use it. In essence, let u=2x+5y-3 and v=3x-7y+8. It should give you a nice coordinate transformation that will change your ellipse to something easily integrable.
     
  4. Jun 23, 2011 #3
    Thanks, it turned out to be really easy!
     
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