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Line integral: physics

  1. Nov 25, 2007 #1
    1. The problem statement, all variables and given/known data

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

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

    2. Relevant equations

    3. The attempt at a solution

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

    Then [tex] dm = 3k \cos t \sin t \ dt [/tex]

    So does [tex] I_0 = 3k\int_{0}^{2 \pi} \left( \cos^{6} t + \sin^{6} t \right)(\cos t \sin t) \ dt = 0 [/tex]?

    Is this correct?
  2. jcsd
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