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Thread: Line integral

  1. #1
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    Line integral

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

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

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

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

    So does $\displaystyle 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; Nov 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 $\displaystyle I_0 = 0 $?
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