- #1
tronter
- 185
- 1
Homework Statement
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]
Homework Equations
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?