Line integral: physics

1. Nov 25, 2007

tronter

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

3. The attempt at a solution

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 $$I_0 = 3k\int_{0}^{2 \pi} \left( \cos^{6} t + \sin^{6} t \right)(\cos t \sin t) \ dt = 0$$?

Is this correct?