Results 1 to 2 of 2

Math Help - iterated integral

  1. #1
    Bop
    Bop is offline
    Junior Member
    Joined
    Dec 2009
    Posts
    48

    iterated integral

    Hello, I want to calculate:

    \int_{A} y d(x,y) where

    A={(x,y): y\ge0; x^2+y^2\le1; x^2+y^2-2x\le0 }

    So:

    \int_{A} y d(x,y) = \int^{1/2}_0 \int^{\sqrt{2x-x^2}}_0 y dy dx + \int^{1}_{1/2} \int^{\sqrt{1-x^2}}_0 y dy dx

    Solving I have:

    \int_{A} y d(x,y) = \frac{5}{24}


    I have tried to solve it with polar coordinate:

    \int_{A} y d(x,y) = \int^{\pi/3}_0 \int^1_0 r^2 sin\theta dr d\theta + \int^{\pi/2}_{\pi/3} \int^{2cos\theta}_1 r^2 sin\theta dr d\theta

    Solving this one I have:

    \int_{A} y d(x,y) = \frac{1}{24}

    As we can see, second result is 5 times the first one, so there must be any mistakes.

    Any suggestions?


    Thank you very much.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Bop
    Bop is offline
    Junior Member
    Joined
    Dec 2009
    Posts
    48
    I have made the graphic with A region, I think maybe there is a mistake with polar coordinate?


    Thank you.
    Attached Thumbnails Attached Thumbnails iterated integral-1.jpeg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Iterated Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 11th 2010, 05:02 AM
  2. Iterated Integral Sketch
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 4th 2010, 01:11 PM
  3. Iterated Integral
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 28th 2010, 06:22 PM
  4. Iterated Integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 25th 2010, 09:20 PM
  5. iterated integral
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: January 24th 2010, 12:26 AM

Search Tags


/mathhelpforum @mathhelpforum