Hi, I am having trouble with the following problem:

Evaluate the integral for

on the curveCconsisting of thex-axis fromx=0 tox=2, the parabola up to they-axis, and they-axis down to the origin.

This is what I did so far:

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

$\displaystyle

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

$

$\displaystyle

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

$

= 64

But, this is not right. Please help me out..

Many thanks.