Integrating Over an Oval: Solving Double Integrals with Non-Circular Boundaries

[rad0786]

Anybody know how to integrate over...

Z^2 = 4x^2 + y^2 with the plane z = 1 ?

this comes from my class notes... hmmm.. the proff did some thing really messy... or at least i wrote it messy...

but i got

0(integral)2pi 0(integral)1 z dz d(pheta)

which doesn't seem to make sense since its an Oval, not a circle.

what would be the limits in polar coords?

 

[James R]

I'm not sure what you're trying to do.

Are you trying to find the area of the curve

$$4x^2 + y^2 = 1$$?

 

[rad0786]

yes.. i suppose its that... but the double integral.
infact, the question asks to find the line integral using stokes therm.

so... just how do you doulbe integrate that equation above? its an oval, so you cannot really use polar coords right?