Calculus III problem [URGENT]

[SolitaryRaf]

Hi, so tomorrow's pretty much the last day of the summer semester for me and I have a homework assignment due tomorrow that's confusing me sooo much..

Im here asking for some help in direction on how to do these problems so that I can find the solution by myself... I would really really appreciate any help anyone could provide ...

I am not sure how to represent the domain as a function, and if anyone could point me in the right direction, I'm sure I could get the answer.

The Problem -

I would really really really appreciate any help at all. I need to know how to represent the domain as a function.

 

[galactus]

Start by finding the partials.

$\displaystyle \frac{\partial}{\partial x}(3xy^{2}-x^{3})-\frac{\partial}{\partial y}(sin(x)-6x^{2}y)=3x^{2}+3y^{2}$

Notice we have $\displaystyle 3(x^{2}+y^{2})$, which can be converted to polar.

$\displaystyle 3\int\int r^{3}drd{\theta}$

Can you find the limits of integration and continue?.

Here is the graph: