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Math Help - Line integral

  1. #1
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    Line integral

    Let  x = \cos^{3} t and  y = \sin^{3}t (  0 \leq t \leq 2 \pi ). Also  \rho(x,y) = k .

    Find  I_0 = \int_{C} (x^{2} + y^{2}) \ dm

    So  m = \int_{C} k \ ds = 3k \int_{0}^{2 \pi} \cos t \sin t \ dt .

    Then  dm = 3k \cos t \sin t \ dt .

    So does  I_0 = 3k\int_{0}^{2 \pi} \left( \cos^{6} t + \sin^{6} t \right)(\cos t \sin t) \ dt = 0
    Last edited by shilz222; November 25th 2007 at 01:13 PM.
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  2. #2
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    So if the work is 0 does this imply that the path is closed?
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  3. #3
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    I don't think it physically makes sense for  I_0 = 0 ?
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