Compute area using divergence and flux?

[nebbie]

Compute area using divergence and flux??

Consider the curve given by g(t) =acos^3(t),asin^3(t), where t is [0; 2pi] and a > 0 is a constant.

(a) Find the unit tangent and outward normal vectors.
(b) Compute the area enclosed by this curve.

I have done part a), and I know that
flux of F = divergence x area
but for part b), i m not given a vector field F. so how am I suppose to approach this question and possibly find the divergence (thus the area)? any hint or solution would be much appreciated. ^__^

 

[Dick]

If you could find an F such the div(F)=1, that would work, right?

 

[nebbie]

If you could find an F such the div(F)=1, that would work, right?

why would the divergence be 1? could you be more specific please?

 

[Dick]

You are going to integrate the divergence over the surface by computing the flux of F around the curve, right? If div(F)=1 then the integral of the divergence is the integral of 1 over the surface. That's the area. So pick ANY F that has div(F)=1. There's lots of choices.