1. ## Green's Theorem Integral

Hi, I am having trouble with the following problem:

Evaluate the integral for

on the curve C consisting of the x-axis from x=0 to x=2, the parabola up to the y-axis, and the y-axis down to the origin.

This is what I did so far:

F(x,y)= <6xy^3,6x^2y^2>

$
\int\int_{D} =[(6x^2y^2)*\frac{\partial}{\partial x}-(6xy^3)\frac{\partial}{\partial y}] dA
$

$
= \int_{0}^{2} \int_{4-x^2}^{0} [12xy^2-18xy^2] dy dx
$

= 64

Many thanks.

2. Originally Posted by althaemenes
Hi, I am having trouble with the following problem:

Evaluate the integral for

on the curve C consisting of the x-axis from x=0 to x=2, the parabola up to the y-axis, and the y-axis down to the origin.

This is what I did so far:

F(x,y)= <6xy^3,6x^2y^2>

$
\int\int_{D} =[(6x^2y^2)*\frac{\partial}{\partial x}-(6xy^3)\frac{\partial}{\partial y}] dA
$

$
= \int_{0}^{2} \int_{4-x^2}^{0} [12xy^2-18xy^2] dy dx
$

= 64

Your limits of integration on $y$ are reversed! XD
It should be $\int_{0}^{2} \int_{0}^{4-x^2} \left[12xy^2-18xy^2\right] \,dy \,dx$