# Green's Theorem

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__ Green's Theorem:__ This theorem gives the relation between the plane, surface and the line integrals.

**Statement:** If R is a closed region in the xy-palne bounded by a simple closed curve C and M (x,y) and N (x,y) are continuous function having the partial derivatives in R then,

**1**. Verify Green's Theorem in the plane for where C is the boundary region enclosed by the parabola y^{2} = x and x^{2} = y.

**Solution:** We shall find the point of intersection of the parabolas

and hence y = 0,1 the point of intersection are (0,0) and (1,1).

= I_{1} I_{2} Along Ao: