Greens theorem boundary of a rectangle

[jonroberts74]

Homework Statement

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

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

Homework Equations

The Attempt at a Solution

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

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

 

[vela]

You miscalculated dQ/dx.

 

[jonroberts74]

You miscalculated dQ/dx.

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

 

[HallsofIvy]

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