# Thread: Line Integrals - is this allowed?!!

1. ## Line Integrals - is this allowed?!!

Let R be a region bounded by the curves:

$y^2-x-1=0$ and $y^2+x-1=0$

I want to verify Green's Theorem in the plane for:

$\oint_{\partial{R}}(y^2+x)\, dx +(xy+1)\, dy$

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For the line integrals part, since the two curves intersect at (-1,0) and (1,0).

Can I use:

$\int_{0}^{0}(y^2+x)\, \frac{dx}{dy} \, dy + (xy+1) \, dy$

In which case they will both be equal to zero and I won't have to integrating?

2. $\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}$

$= y - 2y = -y$

Although it is not zero , i still like to congratulate you because it is an odd

function

In fact , it is equal to $- ( ~y-coordinate~of~the~center~of~mass~) \times (~area~)$