- #1
DryRun
Gold Member
- 838
- 4
Homework Statement
Using Green's theorem, evaluate:
http://s2.ipicture.ru/uploads/20120117/6p57O2HO.jpg
The attempt at a solution
[tex]\frac{\partial P}{\partial y}=3x+2y[/tex]
[tex]\frac{\partial Q}{\partial x}=2y+10x[/tex]
[tex]\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}=7x[/tex]
To do the integration, I'm using the parametric equations of the circle; x= cosθ and y=sinθ
[tex]\int\int 7\cos \theta \,.rdrd\theta[/tex]
The curve C is a circle with centre (1,-2) and radius r=1
I've drawn the graph in my copybook.
Description of circle:
For θ fixed, r varies from r=-2 to r=-3
θ varies from -∏/2 to -∏/2
However, i can't get the correct answer as I'm quite sure that I've got the wrong limits. Usually, i deal with circles with centre (0,0) so it's easier to find the limits for r and θ.
Using Green's theorem, evaluate:
http://s2.ipicture.ru/uploads/20120117/6p57O2HO.jpg
The attempt at a solution
[tex]\frac{\partial P}{\partial y}=3x+2y[/tex]
[tex]\frac{\partial Q}{\partial x}=2y+10x[/tex]
[tex]\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}=7x[/tex]
To do the integration, I'm using the parametric equations of the circle; x= cosθ and y=sinθ
[tex]\int\int 7\cos \theta \,.rdrd\theta[/tex]
The curve C is a circle with centre (1,-2) and radius r=1
I've drawn the graph in my copybook.
Description of circle:
For θ fixed, r varies from r=-2 to r=-3
θ varies from -∏/2 to -∏/2
However, i can't get the correct answer as I'm quite sure that I've got the wrong limits. Usually, i deal with circles with centre (0,0) so it's easier to find the limits for r and θ.