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Finding surface of revolution

  1. Jun 28, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the area of the surface of revolution generated by revolving about the x axis the cardioid x=2cos[itex]\vartheta[/itex]-cos2[itex]\vartheta[/itex],y=2sin[itex]\vartheta[/itex]-sin2[itex]\vartheta[/itex].

    pictures show a cardioid with [itex]\vartheta[/itex]=pi and [itex]\vartheta[/itex]=0.


    2. Relevant equations
    After looking up, the formula to solving this type of equation is:
    s=int(sqrt(dx/dtheta)^2 +sqrt(dy/dtheta)^2)
    and also some trig identities

    3. The attempt at a solution
    Alright, I first went ahead and applied the equation above to the functions, and integrated from 0 to pi (since that is where the edges of the cartoid lie?). However, after going through the math and solving it out, I get a -2/3(sinx*cosx^3/2) from 0 to pi, which makes no sense (since volume will be 0 if this int. is evaluated).

    thanks so much in advance!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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