Solving Green's Theorem Integrals: Finding the Area

[asi123]

Homework Statement

Hey.
I need to use Green's theorem in order to solve this integral.
My question is, how can I find the area for the Green's theorem integral?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

If x= sin t cos t and y= sin² t, then x²+ y²= sin²tcos²t+ sin⁴t= sin² t(cos² t+ sin²t)= sin²(t)= y so the equation, in Cartesian coordinates, is x²+ y²- y= 0. Complete the square and you can see that is a circle.

 

[asi123]

If x= sin t cos t and y= sin² t, then x²+ y²= sin²cos²+ sin[sup4[/sup]= sin² t(cos² t+ sin²t)= sin²(t)= y so the equation, in Cartesian coordinates, is x²+ y²- y= 0. Complete the square and you can see that is a circle.

thanks.