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Homework Help: Simplifying Integral

  1. Jan 30, 2008 #1
    Hello
    Here is an integral question I have. It's a surface area problem, but i just have issues simplifying the square root before solving. Any help appreciated!

    y=(1-x[tex]^{2/3}[/tex])[tex]^{3/2}[/tex], 0[tex]\leq[/tex]x[tex]\leq[/tex]1

    My work:
    dy/dx=-x[tex]^{-1/3}[/tex](1-x[tex]^{2/3}[/tex])[tex]^{1/2}[/tex]
    (dy/dx)[tex]^{2}[/tex]=-x[tex]^{-2/3}[/tex](1-x[tex]^{2/3}[/tex])
    =-x[tex]^{-2/3}[/tex]+1



    S=(insert integral with limits here) 2[tex]\pi[/tex]xds
    =2[tex]\pi[/tex]x [tex]\sqrt{-x^{-2/3} +1+1}[/tex]
    =2[tex]\pi[/tex]x [tex]\sqrt{-x^{-2/3} +2}[/tex]

    I'm not sure where to go after this...
    thx
     
    Last edited: Jan 30, 2008
  2. jcsd
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