# Homework Help: Greens theorem boundary of a rectangle

1. Aug 1, 2014

### jonroberts74

1. The problem statement, all variables and given/known data

$\mathscr{C}: x=1,x=3,y=2,y=3$

$\int_\mathscr{C} (xy^2-y^3)dx+(-5x^2+y^3)dy$

2. Relevant equations

3. The attempt at a solution

$\frac{\partial Q}{\partial x} = -10x^2 \,\,; \frac{\partial P}{\partial y} = 2xy-3y^2$

$\int\int_\mathscr{C} \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} dA = \displaystyle \int_{2}^{3}\int_{1}^{3} (-10x^2-2xy+3y^2)dxdy = -\frac{206}{3}$

2. Aug 1, 2014

### vela

Staff Emeritus
You miscalculated dQ/dx.

3. Aug 1, 2014

### jonroberts74

oh haha, -10x not $-10x^2$ thanks

4. Aug 2, 2014

### HallsofIvy

Of course, it is easy to do the integration around the path directly as a check. Have you done that?