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Volume of solid formed by revolution of one loop of Lemniscate of bernoulli

  1. Sep 24, 2008 #1
    Hello ppl. I have a problem in finding out the volume of solid formed by the revolution of one loop of lemniscate of bernoulli ( r²=a²cos2θ) about the initial line θ =0



    Using the relevant forumula for the volume of the solid generated by the revolution of one loop of the polar curve about the initial line,

    [​IMG] ,

    where V is the volume of the solid and π/4 and 0 are the upper and lower limits respectively.




    In this problem ,

    [​IMG]

    But i am not able to integrate further. I am kinda stuck here. What substitution should i take?Please help me.
     
    Last edited: Sep 24, 2008
  2. jcsd
  3. Sep 24, 2008 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    Try using the following trig identity:

    [tex]cos(2 \theta )=2cos^2( \theta )-1[/tex]

    And then use a substitution like [tex]u \equiv \sqrt{2} cos( \theta ) [/tex]
     
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